Twisted K-theory of differentiable stacks
Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 37 (2004) no. 6, pp. 841-910.
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Tu, Jean-Louis; Xu, Ping; Laurent-Gengoux, Camille. Twisted $K$-theory of differentiable stacks. Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 37 (2004) no. 6, pp. 841-910. doi : 10.1016/j.ansens.2004.10.002. http://archive.numdam.org/articles/10.1016/j.ansens.2004.10.002/

[1] Adem A., Ruan Y., Twisted orbifold K-theory, Comm. Math. Phys. 237 (2003) 533-556. | MR | Zbl

[2] Artin M. et al. , Théorie des topos et cohomologie étale des schémas, in: Séminaire de géométrie algébrique, Lecture Notes in Mathematics, vols. 269, 270, 305, Springer, Berlin, 1972-1973.

[3] Atiyah M., K-theory. Lecture notes by D.W. Anderson, 1967. | MR

[4] Atiyah M., K-theory past and present, math.KT/0012213. | MR

[5] Atiyah M., Segal G., Twisted K-theory, math.KT/0407054.

[6] Baum P., Connes A., Chern character for discrete groups, in: A fête of topology, Academic Press, New York, 1988, pp. 163-232. | MR | Zbl

[7] Baum P., Connes A., Higson N., Classifying space for proper actions and K-theory of group C*-algebras, in: C*-Algebras: 1943-1993 (San Antonio, TX, 1993), Contemp. Math., vol. 167, Amer. Math. Soc., Providence, RI, 1994, pp. 240-291. | MR | Zbl

[8] Behrend K., Edidin B., Fantechi B., Fulton W., Gottsche L., Kresch K., Introduction to stacks, in preparation.

[9] Behrend K., Xu P., S1-bundles and gerbes over differentiable stack, C. R. Acad. Sci. Paris Sér. I 336 (2003) 163-168. | MR | Zbl

[10] Behrend, K., Xu P., Differentiable stacks and gerbes, in preparation.

[11] Blackadar B., K-Theory for Operator Algebras, Mathematical Sciences Research Institute Publications, vol. 5, Cambridge University Press, Cambridge, 1998. | MR | Zbl

[12] Blanchard E., Déformations de C*-algèbres de Hopf, Bull. Soc. Math. France 124 (1996) 141-215. | Numdam | MR | Zbl

[13] Bost J.-B., Principe d'Oka, K-théorie et systèmes dynamiques non commutatifs, Invent. Math. 101 (1990) 261-333. | MR | Zbl

[14] Brylinski J.-L., Loop Spaces, Characteristic Classes and Geometric Quantization, Progress in Mathematics, vol. 107, Birkhäuser, Basel, 1993. | MR | Zbl

[15] Bouwknegt P., Mathai V., D-branes, B-fields and twisted K-theory, J. High Energy Phys. 3 (2000) 7-11. | MR | Zbl

[16] Bouwknegt P., Carey A., Mathai V., Murray M., Stevenson D., Twisted K-theory and K-theory of bundle gerbes, Comm. Math. Phys. 228 (2002) 17-45. | MR | Zbl

[17] Connes A., Cyclic Cohomology and the Transverse Fundamental Class of a Foliation, in: Pitman Research Notes Math. Ser., vol. 123, Longman Sci., Harlow, 1986, pp. 52-144. | MR | Zbl

[18] Connes A., Skandalis G., The longitudinal index theorem for foliations, Publ. Res. Inst. Math. Sci. Kyoto Univ. 20 (1984) 1139-1183. | MR | Zbl

[19] Crainic M., Differentiable and algebroid cohomology, van Est isomorphisms, and characteristic classes, Comment. Math. Helv. 78 (2003) 681-721. | MR | Zbl

[20] Crainic M., Moerdijk I., A homology theory for étale groupoids, J. Reine Angew. Math. 521 (2000) 25-46. | MR | Zbl

[21] Dixmier J., C*-Algebras, North Holland, Amsterdam, 1977. | MR | Zbl

[22] Dixmier J., Douady A., Champs continus d’espaces hilbertiens et de C*-algèbres, Bull. Soc. Math. France 91 (1963) 227-284. | Numdam | MR | Zbl

[23] Donovan P., Karoubi M., Graded Brauer groups and K-theory with local coefficients, Inst. Hautes Études Sci. Publ. 38 (1970) 5-25. | Numdam | MR | Zbl

[24] Dupont J., Curvature and Characteristic Classes, Lecture Notes in Mathematics, vol. 640, Springer, Berlin, 1978. | MR | Zbl

[25] Dupré M.J., Gillette R.M., Banach Bundles, Banach Modules and Automorphisms of C*-Algebras, Pitman Research Notes in Mathematics, vol. 92, 1983. | MR | Zbl

[26] Fell J., Doran R., Representations of C*-Algebras, Locally Compact Groups, and Banach ∗-Algebraic Bundles, vol. 2, Pure and Applied Mathematics, vol. 126, Academic Press, Boston, MA, 1988. | Zbl

[27] Freed D., The Verlinde algebra is twisted equivariant K-theory, Turkish J. Math. 25 (2001) 159-167. | MR | Zbl

[28] Fulman I., Muhly P., Bimodules, spectra, and Fell bundles, Israel J. Math. 108 (1998) 193-215. | MR | Zbl

[29] Gabriel P., Zisman M., Calculus of Fractions and Homotopy Theory, Ergebnisse der Mathematik und ihrer Grenzgebiete, vol. 35, Springer, Berlin, 1967. | MR | Zbl

[30] Giraud J., Cohomologie non abélienne, Die Grundlehren der mathematischen Wissenschaften, vol. 179, Springer, Berlin, 1971. | MR | Zbl

[31] Grothendieck A., Le groupe de Brauer, Séminaire Bourbaki (1964/65), Collection Hors Série de la S.M.F. 9 (1995) 199-219. | Numdam | MR | Zbl

[32] Guillemin V., Sternberg S., Supersymmetry and Equivariant de Rham Theory, Springer, Berlin, 1999. | MR | Zbl

[33] Haefliger A., Groupoïdes d'holonomie et classifiants, Astérisque 116 (1984) 70-97. | Numdam | MR | Zbl

[34] Higson N., On a technical theorem of Kasparov, J. Funct. Anal. 73 (1987) 107-112. | MR | Zbl

[35] Higson N., The Baum-Connes conjecture, in: Proceedings of the International Congress of Mathematicians, vol. II (Berlin, 1998), Doc. Math., Extra vol. II, 1998, pp. 637-646, (electronic). | MR | Zbl

[36] Higson N., Lafforgue V., Skandalis G., Counterexamples to the Baum-Connes conjecture, Geom. Funct. Anal. 12 (2) (2002) 330-354. | MR | Zbl

[37] Higson N., Roe J., Yu G., A coarse Mayer-Vietoris principle, Math. Proc. Cambridge Philos. Soc. 114 (1993) 85-97. | MR | Zbl

[38] Hilsum M., Skandalis G., Morphismes K-orientés d'espaces de feuilles et fonctorialité en théorie de Kasparov (d'après une conjecture d'A. Connes), Ann. Sci. Éc. Norm. Sup. 20 (1987) 325-390. | Numdam | MR | Zbl

[39] Hitchin N., Lectures on special Lagrangian submanifolds, AMS/IP Stud. Adv. Math. 23 (1999) 151-182. | MR | Zbl

[40] Kellendonk J., Noncommutative geometry of tilings and gap labelling, Rev. Math. Phys. 7 (7) (1995) 1133-1180. | MR | Zbl

[41] Koosis P., An irreducible unitary representation of a compact group is finite dimensional, Proc. Amer. Math. Soc. 8 (1957) 712-715. | MR | Zbl

[42] Kumjian A., Fell Bundles over groupoids, Proc. Amer. Math. Soc. 128 (1998) 1115-1125. | MR | Zbl

[43] Kumjian A., Muhly P., Renault J., Williams D., The Brauer group of a locally compact groupoid, Amer. J. Math. 120 (1998) 901-954. | MR | Zbl

[44] Le Gall P.-Y., Théorie de Kasparov équivariante et groupoïdes, 16 (1999) 361-390. | MR | Zbl

[45] Lupercio E., Uribe B., Gerbes over orbifolds and twisted K-theory, Comm. Math. Phys. 245 (2004) 449-489. | MR | Zbl

[46] Mathai V., Stevenson D., Chern character in twisted K-theory, equivariant and holomorphic cases, Comm. Math. Phys. 236 (2003) 161-186. | MR | Zbl

[47] Meinrenken E., The basic gerbe over a compact simple Lie group, Enseign. Math. (2) 49 (2003) 307-333. | MR | Zbl

[48] Mickelsson J., Gerbes, (twisted) K-theory, and the supersymmetric WZW model, hep-th/0206139.

[49] Minasian R., Moore G., K-theory and Ramond-Ramond charge, J. High Energy Phys. 11 (1997) 2-7. | MR | Zbl

[50] Monthubert B., Groupoids of manifolds with corners and index theory, in: Groupoids in Analysis, Geometry, and Physics (Boulder, CO, 1999), Contemp. Math., vol. 282, Amer. Math. Soc., Providence, RI, 2001, pp. 147-157. | MR | Zbl

[51] Mrčun J., Functoriality of the bimodule associated to a Hilsum-Skandalis map, 18 (1999) 235-253. | MR | Zbl

[52] Moerdijk I., Orbifolds as groupoids: an introduction, in: Orbifolds in Mathematics and Physics (Madison, WI, 2001), Contemp. Math., vol. 310, 2002, pp. 205-222. | MR | Zbl

[53] Moerdijk I., Introduction to the language of stacks and gerbes, math.AT/0212266.

[54] Moerdijk I., Pronk D.A., Orbifolds, sheaves and groupoids, 12 (1997) 3-21. | MR | Zbl

[55] Muhly P., Bundles over groupoids, in: Groupoids in Analysis, Geometry and Physics (Boulder, CO, 1999), Contemp. Math., vol. 282, Amer. Math. Soc., Providence, RI, 2000, pp. 67-82. | MR | Zbl

[56] Muhly P., Renault J., Williams D., Equivalence and isomorphism for groupoid C*-algebras, J. Operator Theory 17 (1987) 3-22. | MR | Zbl

[57] Paterson A., The analytic index for proper, Lie groupoid actions, in: Groupoids in Analysis, Geometry, and Physics (Boulder, CO, 1999), Contemp. Math., vol. 282, Amer. Math. Soc., Providence, RI, 2001, pp. 115-135. | MR | Zbl

[58] Pedersen G., C*-Algebras and their Automorphism Groups, London Mathematical Society Monographs, vol. 14, Academic Press, London, 1979. | MR | Zbl

[59] Pressley A., Segal G., Loop Groups, Oxford Mathematical Monographs, Oxford University Press, New York, 1986. | MR | Zbl

[60] Raeburn I., Taylor J., Continuous trace C*-algebras with given Dixmier-Douady class, J. Austral. Math. Soc. Ser. A 38 (1985) 394-407. | MR | Zbl

[61] Renault J., A Groupoid Approach to C*-Algebras, Lecture Notes in Mathematics, vol. 793, Springer, Berlin, 1980. | MR | Zbl

[62] Renault J., Représentation des produits croisés d'algèbres de groupoïdes, J. Operator Theory 18 (1987) 67-97. | MR | Zbl

[63] Rosenberg J., Continuous-trace algebras from the bundle theoretic point of view, J. Austral. Math. Soc. Ser. A 47 (1989) 368-381. | MR | Zbl

[64] Schweitzer L.B., A short proof that MnA is local if A is local and Fréchet, Internat. J. Math. 3 (4) (1992) 581-589. | MR | Zbl

[65] Segal G., Equivariant K-theory, Inst. Hautes Études Sci. Publ. Math. 34 (1968) 129-151. | Numdam | MR | Zbl

[66] Segal G., Fredholm complexes, Quart. J. Math. Oxford Ser. (2) 21 (1970) 385-402. | MR | Zbl

[67] Skandalis G., Tu J.L., Yu G., The coarse Baum-Connes conjecture and groupoids, Topology 41 (4) (2002) 807-834. | MR | Zbl

[68] Tu J.-L., La conjecture de Novikov pour les feuilletages hyperboliques, 16 (1999) 129-184. | MR | Zbl

[69] Tu J.-L., La conjecture de Baum-Connes pour les feuilletages moyennables, 17 (3) (1999) 215-264. | MR | Zbl

[70] Tuynman G.M., Wiegerinck G.M., Central extensions and physics, J. Geom. Phys. 4 (1987) 207-258. | MR | Zbl

[71] Yamagami S., On primitive ideal spaces of C*-algebras over certain locally compact groupoids, in: Mappings of Operator Algebras (Philadelphia, PA, 1988), Progress in Math., vol. 84, Birkhäuser Boston, Boston, MA, 1990, pp. 199-204. | MR | Zbl

[72] Wegge-Olsen N.E., K-theory and C*-algebras, A friendly approach, Oxford Science Publications, The Clarendon Press, Oxford University Press, New York, 1993. | MR | Zbl

[73] Weil A., Sur les théorèmes de De Rham, Comment. Math. Helv. 26 (1959) 119-145. | MR | Zbl

[74] Weinstein A., Xu P., Extensions of symplectic groupoids and quantization, J. Reine Angew. Math. 417 (1991) 159-189. | MR | Zbl

[75] Witten E., D-branes and K-theory, J. High Energy Phys. 12 (1998) 19-44. | MR | Zbl

[76] Witten E., Overview of K-theory applied to strings, Internat. J. Modern Phys. A 16 (2001) 693-706. | MR | Zbl

[77] Xu P., Morita equivalent symplectic groupoids, Math. Sci. Res. Inst. Publ. 20 (1991) 291-311. | MR | Zbl

  • Dove, Tom; Schick, Thomas Equivariant topological T-duality, Communications in Mathematical Physics, Volume 405 (2024) no. 8, p. 35 (Id/No 179) | DOI:10.1007/s00220-024-05044-0 | Zbl:7895046
  • Biswas, Indranil; Chatterjee, Saikat; Koushik, Praphulla; Neumann, Frank Connections on Lie groupoids and Chern-Weil theory, Reviews in Mathematical Physics, Volume 36 (2024) no. 3, p. 42 (Id/No 2450002) | DOI:10.1142/s0129055x24500028 | Zbl:1541.53032
  • Baldare, Alexandre The index of families of projective operators, Annals of K-Theory, Volume 8 (2023) no. 3, p. 285 | DOI:10.2140/akt.2023.8.285
  • Biswas, Indranil; Chatterjee, Saikat; Koushik, Praphulla; Neumann, Frank Atiyah sequences and connections on principal bundles over Lie groupoids and differentiable stacks, Journal of Noncommutative Geometry, Volume 17 (2023) no. 2, pp. 407-437 | DOI:10.4171/jncg/486 | Zbl:1520.53018
  • Bárcenas, Noé; Velásquez, Mario The completion theorem in twisted equivariant K-theory for proper actions, Journal of Homotopy and Related Structures, Volume 17 (2022) no. 1, pp. 77-104 | DOI:10.1007/s40062-021-00299-z | Zbl:1525.19002
  • Loizides, Yiannis Geometric K-homology and the Freed-Hopkins-Teleman theorem, Journal of Noncommutative Geometry, Volume 16 (2022) no. 1, pp. 77-118 | DOI:10.4171/jncg/447 | Zbl:1490.19012
  • Bönicke, Christian K-theory and homotopies of twists on ample groupoids, Journal of Noncommutative Geometry, Volume 15 (2021) no. 1, pp. 195-222 | DOI:10.4171/jncg/399 | Zbl:1477.46077
  • MacDonald, Lachlan E. Equivariant KK-theory for non-Hausdorff groupoids, Journal of Geometry and Physics, Volume 154 (2020), p. 16 (Id/No 103709) | DOI:10.1016/j.geomphys.2020.103709 | Zbl:1444.22002
  • Benameur, Moulay-Tahar; Roy, Indrava The Higson-Roe sequence for étale groupoids. I: Dual algebras and compatibility with the BC map, Journal of Noncommutative Geometry, Volume 14 (2020) no. 1, pp. 25-71 | DOI:10.4171/jncg/358 | Zbl:1444.19008
  • Kubota, Yosuke The relative Mishchenko-Fomenko higher index and almost flat bundles. I: The relative Mishchenko-Fomenko index, Journal of Noncommutative Geometry, Volume 14 (2020) no. 3, pp. 1209-1244 | DOI:10.4171/jncg/391 | Zbl:1469.19010
  • Bárcenas, Noé Twisted geometric K-homology for proper actions of discrete groups, Journal of Topology and Analysis, Volume 12 (2020) no. 4, pp. 1019-1040 | DOI:10.1142/s1793525319500729 | Zbl:1452.19001
  • Bunke, Ulrich; Nikolaus, Thomas Twisted differential cohomology, Algebraic Geometric Topology, Volume 19 (2019) no. 4, pp. 1631-1710 | DOI:10.2140/agt.2019.19.1631 | Zbl:1447.55005
  • Grady, Daniel; Sati, Hisham Twisted differential generalized cohomology theories and their Atiyah-Hirzebruch spectral sequence, Algebraic Geometric Topology, Volume 19 (2019) no. 6, pp. 2899-2960 | DOI:10.2140/agt.2019.19.2899 | Zbl:1427.19006
  • Austin, Kyle; Georgescu, Magdalena C. Inverse systems of groupoids, with applications to groupoid C-algebras, Journal of Functional Analysis, Volume 276 (2019) no. 3, pp. 716-750 | DOI:10.1016/j.jfa.2018.05.013 | Zbl:1416.46054
  • Krepski, Derek Groupoid equivariant prequantization, Communications in Mathematical Physics, Volume 360 (2018) no. 1, pp. 169-195 | DOI:10.1007/s00220-017-3080-x | Zbl:1454.22001
  • Benameur, Moulay-Tahar; Gorokhovsky, Alexander; Leichtnam, Eric The higher twisted index theorem for foliations, Journal of Functional Analysis, Volume 273 (2017) no. 2, pp. 496-558 | DOI:10.1016/j.jfa.2017.03.009 | Zbl:1402.58017
  • Alsulami, Samirah; Colman, Hellen; Neumann, Frank The Lusternik-Schnirelmann category for a differentiable stack, Mathematics across contemporary sciences. AUS-ICMS, American University of Sharjah, United Arab Emirates, April 2–5, 2015, Cham: Springer, 2017, pp. 1-15 | DOI:10.1007/978-3-319-46310-0_1 | Zbl:1421.55001
  • Bárcenas, Noé; Carrillo Rouse, Paulo; Velásquez, Mario Multiplicative structures and the twisted Baum-Connes assembly map, Transactions of the American Mathematical Society, Volume 369 (2017) no. 7, pp. 5241-5269 | DOI:10.1090/tran/7024 | Zbl:1360.19010
  • Kubota, Yosuke Notes on twisted equivariant K-theory for C-algebras, International Journal of Mathematics, Volume 27 (2016) no. 6, p. 28 (Id/No 1650058) | DOI:10.1142/s0129167x16500580 | Zbl:1347.19001
  • Hekmati, Pedram; Mickelsson, Jouko Projective families of Dirac operators on a Banach Lie groupoid, Journal of Noncommutative Geometry, Volume 10 (2016) no. 1, pp. 1-28 | DOI:10.4171/jncg/227 | Zbl:1337.22010
  • Bytsenko, Andrey A; Szabo, Richard J; Tureanu, Anca Stratified fiber bundles, Quinn homology and brane stability of hyperbolic orbifolds, Journal of Physics A: Mathematical and Theoretical, Volume 49 (2016) no. 16, p. 165401 | DOI:10.1088/1751-8113/49/16/165401
  • Farsi, Carla; Gillaspy, Elizabeth Twists over étale groupoids and twisted vector bundles, Proceedings of the American Mathematical Society, Volume 144 (2016) no. 9, pp. 3767-3779 | DOI:10.1090/proc/13165 | Zbl:1421.46045
  • Williams, Dana P. Haar systems on equivalent groupoids, Proceedings of the American Mathematical Society. Series B, Volume 3 (2016), pp. 1-8 | DOI:10.1090/bproc/22 | Zbl:1341.22002
  • Gillaspy, Elizabeth K-theory and homotopies of 2-cocycles on group bundles, Rocky Mountain Journal of Mathematics, Volume 46 (2016) no. 4, pp. 1207-1229 | DOI:10.1216/rmj-2016-46-4-1207 | Zbl:1357.46065
  • Nikolaus, Thomas; Schreiber, Urs; Stevenson, Danny Principal -bundles: presentations, Journal of Homotopy and Related Structures, Volume 10 (2015) no. 3, pp. 565-622 | DOI:10.1007/s40062-014-0077-4 | Zbl:1344.18002
  • Sati, Hisham; Westerland, Craig Twisted Morava K-theory and E-theory, Journal of Topology, Volume 8 (2015) no. 4, pp. 887-916 | DOI:10.1112/jtopol/jtv020 | Zbl:1330.55007
  • Gillaspy, Elizabeth K-theory and homotopies of 2-cocycles on higher-rank graphs, Pacific Journal of Mathematics, Volume 278 (2015) no. 2, p. 407 | DOI:10.2140/pjm.2015.278.407
  • Tang, Xiang; Tseng, Hsian-Hua Duality theorems for étale gerbes on orbifolds, Advances in Mathematics, Volume 250 (2014), pp. 496-569 | DOI:10.1016/j.aim.2013.10.002 | Zbl:1300.14058
  • Tang, Xiang; Tseng, Hsian-Hua Conjugacy classes and characters for extensions of finite groups., Chinese Annals of Mathematics. Series B, Volume 35 (2014) no. 5, pp. 743-750 | DOI:10.1007/s11401-014-0854-8 | Zbl:1318.20029
  • Moutuou, El-kaïoum M. Graded Brauer groups of a groupoid with involution, Journal of Functional Analysis, Volume 266 (2014) no. 5, pp. 2689-2739 | DOI:10.1016/j.jfa.2013.12.019 | Zbl:1343.22002
  • Harju, Antti J. Twisted K-theory constructions in the case of a decomposable Dixmier-Douady class. II: Topological and equivariant models, Journal of Geometry and Physics, Volume 82 (2014), pp. 46-63 | DOI:10.1016/j.geomphys.2014.04.002 | Zbl:1327.19013
  • Moutuou, El-Kaïoum M. Equivariant KK-theory for generalised actions and Thom isomorphism in groupoid twisted K-theory, Journal of K-Theory, Volume 13 (2014) no. 1, p. 83 | DOI:10.1017/is013010018jkt244
  • Mahanta, Snigdhayan Twisted K-theory, K-homology, and bivariant Chern-Connes type character of some infinite dimensional spaces, Kyoto Journal of Mathematics, Volume 54 (2014) no. 3, pp. 597-640 | DOI:10.1215/21562261-2693460 | Zbl:1309.19006
  • Freed, Daniel S.; Moore, Gregory W. Twisted equivariant matter, Annales Henri Poincaré, Volume 14 (2013) no. 8, pp. 1927-2023 | DOI:10.1007/s00023-013-0236-x | Zbl:1286.81109
  • Landweber, Gregory D.; Sjamaar, Reyer Character formulæ and GKRS multiplets in equivariant K-theory, Selecta Mathematica. New Series, Volume 19 (2013) no. 1, pp. 49-95 | DOI:10.1007/s00029-012-0102-6 | Zbl:1267.19006
  • Hu, Jianxun; Wang, Bai-Ling Delocalized Chern character for stringy orbifold K-theory, Transactions of the American Mathematical Society, Volume 365 (2013) no. 12, pp. 6309-6341 | DOI:10.1090/s0002-9947-2013-05834-5 | Zbl:1278.19011
  • Spitzweck, Markus; Østvær, Paul Arne Motivic twisted K-theory, Algebraic Geometric Topology, Volume 12 (2012) no. 1, pp. 565-599 | DOI:10.2140/agt.2012.12.565 | Zbl:1282.14040
  • Bunke, Ulrich; Schick, Thomas Differential K-theory: a survey, Global differential geometry, Berlin: Springer, 2012, pp. 303-357 | DOI:10.1007/978-3-642-22842-1_11 | Zbl:1245.19002
  • Bressler, Paul; Gorokhovsky, Alexander; Nest, Ryszard; Tsygan, Boris Deformations of algebroid stacks, Advances in Mathematics, Volume 226 (2011) no. 4, pp. 3018-3087 | DOI:10.1016/j.aim.2010.10.008 | Zbl:1209.53062
  • Carrillo Rouse, Paulo; Wang, Bai-Ling Twisted longitudinal index theorem for foliations and wrong way functoriality, Advances in Mathematics, Volume 226 (2011) no. 6, pp. 4933-4986 | DOI:10.1016/j.aim.2010.12.026 | Zbl:1222.58016
  • Bartlett, Bruce The geometry of unitary 2-representations of finite groups and their 2-characters, Applied Categorical Structures, Volume 19 (2011) no. 1, pp. 175-232 | DOI:10.1007/s10485-009-9189-0 | Zbl:1220.57019
  • Gomi, Kiyonori; Terashima, Yuji Chern-Weil construction for twisted K-theory, Communications in Mathematical Physics, Volume 299 (2010) no. 1, pp. 225-254 | DOI:10.1007/s00220-010-1080-1 | Zbl:1204.19006
  • Carrillo Rouse, Paulo; Wang, Bai-Ling Twisted index theory for foliations, Comptes Rendus. Mathématique. Académie des Sciences, Paris, Volume 348 (2010) no. 23-24, pp. 1297-1301 | DOI:10.1016/j.crma.2010.10.037 | Zbl:1232.58012
  • Laurent-Gengoux, Camille; Stiénon, Mathieu; Xu, Ping Non-abelian differentiable gerbes, Advances in Mathematics, Volume 220 (2009) no. 5, pp. 1357-1427 | DOI:10.1016/j.aim.2008.10.018 | Zbl:1177.22001
  • Tu, Jean-Louis; Xu, Ping The ring structure for equivariant twisted K-theory, Journal für die Reine und Angewandte Mathematik, Volume 635 (2009), pp. 97-148 | DOI:10.1515/crelle.2009.077 | Zbl:1180.19004
  • Emerson, Heath; Meyer, Ralf Equivariant representable K-theory, Journal of Topology, Volume 2 (2009) no. 1, pp. 123-156 | DOI:10.1112/jtopol/jtp003 | Zbl:1163.19003
  • Tu, Jean-Louis Twisted K-theory and Poincaré duality, Transactions of the American Mathematical Society, Volume 361 (2009) no. 3, pp. 1269-1278 | DOI:10.1090/s0002-9947-08-04706-5 | Zbl:1173.46052
  • Alldridge, Alexander; Johansen, Troels Roussau An index theorem for Wiener-Hopf operators, Advances in Mathematics, Volume 218 (2008) no. 1, pp. 163-201 | DOI:10.1016/j.aim.2007.11.024 | Zbl:1141.47044
  • Laurent-Gengoux, Camille; Wagemann, Friedrich Obstruction classes of crossed modules of Lie algebroids and Lie groupoids linked to existence of principal bundles, Annals of Global Analysis and Geometry, Volume 34 (2008) no. 1, pp. 21-37 | DOI:10.1007/s10455-007-9098-0 | Zbl:1146.55012
  • Blohmann, Christian Stacky Lie Groups, International Mathematics Research Notices, Volume 2008 (2008) | DOI:10.1093/imrn/rnn082
  • Tähtinen, Vesa Anomalies in gauge theory and gerbes over quotient stacks, Journal of Geometry and Physics, Volume 58 (2008) no. 9, pp. 1080-1100 | DOI:10.1016/j.geomphys.2008.03.010 | Zbl:1157.53017
  • Carey, Alan L.; Wang, Bai-Ling Thom isomorphism and push-forward map in twisted K-theory, Journal of K-Theory, Volume 1 (2008) no. 2, p. 357 | DOI:10.1017/is007011015jkt011
  • Pan, Jianzhong; Ruan, Yongbin; Yin, Xiaoqin Gerbes and twisted orbifold quantum cohomology, Science in China. Series A, Volume 51 (2008) no. 6, pp. 995-1016 | DOI:10.1007/s11425-007-0154-9 | Zbl:1146.53069
  • Dwyer, Christopher Twisted equivariant K-theory for proper actions of discrete groups, K-Theory, Volume 38 (2008) no. 2, pp. 95-111 | DOI:10.1007/s10977-007-9016-z | Zbl:1141.19004
  • Bunke, Ulrich; Schick, Thomas; Spitzweck, Markus Sheaf theory for stacks in manifolds and twisted cohomology for S1-gerbes, Algebraic Geometric Topology, Volume 7 (2007), pp. 1007-1062 | DOI:10.2140/agt.2007.7.1007 | Zbl:1149.14002
  • Laurent-Gengoux, Camille; Tu, Jean-Louis; Xu, Ping Chern-Weil map for principal bundles over groupoids, Mathematische Zeitschrift, Volume 255 (2007) no. 3, pp. 451-491 | DOI:10.1007/s00209-006-0004-4 | Zbl:1118.53017
  • Tu, Jean-Louis; Xu, Ping Chern character for twisted K-theory of orbifolds, Advances in Mathematics, Volume 207 (2006) no. 2, pp. 455-483 | DOI:10.1016/j.aim.2005.12.001 | Zbl:1113.19005
  • Tu, Jean-Louis Groupoid cohomology and extensions, Transactions of the American Mathematical Society, Volume 358 (2006) no. 11, pp. 4721-4747 | DOI:10.1090/s0002-9947-06-03982-1 | Zbl:1113.22002

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