@article{ASENS_2004_4_37_6_841_0, author = {Tu, Jean-Louis and Xu, Ping and Laurent-Gengoux, Camille}, title = {Twisted $K$-theory of differentiable stacks}, journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure}, pages = {841--910}, publisher = {Elsevier}, volume = {Ser. 4, 37}, number = {6}, year = {2004}, doi = {10.1016/j.ansens.2004.10.002}, zbl = {1069.19006}, language = {en}, url = {http://archive.numdam.org/articles/10.1016/j.ansens.2004.10.002/} }
TY - JOUR AU - Tu, Jean-Louis AU - Xu, Ping AU - Laurent-Gengoux, Camille TI - Twisted $K$-theory of differentiable stacks JO - Annales scientifiques de l'École Normale Supérieure PY - 2004 SP - 841 EP - 910 VL - 37 IS - 6 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.ansens.2004.10.002/ DO - 10.1016/j.ansens.2004.10.002 LA - en ID - ASENS_2004_4_37_6_841_0 ER -
%0 Journal Article %A Tu, Jean-Louis %A Xu, Ping %A Laurent-Gengoux, Camille %T Twisted $K$-theory of differentiable stacks %J Annales scientifiques de l'École Normale Supérieure %D 2004 %P 841-910 %V 37 %N 6 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.ansens.2004.10.002/ %R 10.1016/j.ansens.2004.10.002 %G en %F ASENS_2004_4_37_6_841_0
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] Twisted orbifold K-theory, Comm. Math. Phys. 237 (2003) 533-556. | MR | Zbl
, ,[2] 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.
et al. ,[3] K-theory. Lecture notes by D.W. Anderson, 1967. | MR
,[4] K-theory past and present, math.KT/0012213. | MR
,[5] Twisted K-theory, math.KT/0407054.
, ,[6] Chern character for discrete groups, in: A fête of topology, Academic Press, New York, 1988, pp. 163-232. | MR | Zbl
, ,
[7] Classifying space for proper actions and K-theory of group
[8] Behrend K., Edidin B., Fantechi B., Fulton W., Gottsche L., Kresch K., Introduction to stacks, in preparation.
[9]
[10] Behrend, K., Xu P., Differentiable stacks and gerbes, in preparation.
[11] K-Theory for Operator Algebras, Mathematical Sciences Research Institute Publications, vol. 5, Cambridge University Press, Cambridge, 1998. | MR | Zbl
,
[12] Déformations de
[13] Principe d'Oka, K-théorie et systèmes dynamiques non commutatifs, Invent. Math. 101 (1990) 261-333. | MR | Zbl
,[14] Loop Spaces, Characteristic Classes and Geometric Quantization, Progress in Mathematics, vol. 107, Birkhäuser, Basel, 1993. | MR | Zbl
,[15] D-branes, B-fields and twisted K-theory, J. High Energy Phys. 3 (2000) 7-11. | MR | Zbl
, ,[16] Twisted K-theory and K-theory of bundle gerbes, Comm. Math. Phys. 228 (2002) 17-45. | MR | Zbl
, , , , ,[17] 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] The longitudinal index theorem for foliations, Publ. Res. Inst. Math. Sci. Kyoto Univ. 20 (1984) 1139-1183. | MR | Zbl
, ,[19] Differentiable and algebroid cohomology, van Est isomorphisms, and characteristic classes, Comment. Math. Helv. 78 (2003) 681-721. | MR | Zbl
,[20] A homology theory for étale groupoids, J. Reine Angew. Math. 521 (2000) 25-46. | MR | Zbl
, ,
[21]
[22] Champs continus d’espaces hilbertiens et de
[23] Graded Brauer groups and K-theory with local coefficients, Inst. Hautes Études Sci. Publ. 38 (1970) 5-25. | Numdam | MR | Zbl
, ,[24] Curvature and Characteristic Classes, Lecture Notes in Mathematics, vol. 640, Springer, Berlin, 1978. | MR | Zbl
,
[25] Banach Bundles, Banach Modules and Automorphisms of
[26] Representations of
[27] The Verlinde algebra is twisted equivariant K-theory, Turkish J. Math. 25 (2001) 159-167. | MR | Zbl
,[28] Bimodules, spectra, and Fell bundles, Israel J. Math. 108 (1998) 193-215. | MR | Zbl
, ,[29] Calculus of Fractions and Homotopy Theory, Ergebnisse der Mathematik und ihrer Grenzgebiete, vol. 35, Springer, Berlin, 1967. | MR | Zbl
, ,[30] Cohomologie non abélienne, Die Grundlehren der mathematischen Wissenschaften, vol. 179, Springer, Berlin, 1971. | MR | Zbl
,[31] Le groupe de Brauer, Séminaire Bourbaki (1964/65), Collection Hors Série de la S.M.F. 9 (1995) 199-219. | Numdam | MR | Zbl
,[32] Supersymmetry and Equivariant de Rham Theory, Springer, Berlin, 1999. | MR | Zbl
, ,[33] Groupoïdes d'holonomie et classifiants, Astérisque 116 (1984) 70-97. | Numdam | MR | Zbl
,[34] On a technical theorem of Kasparov, J. Funct. Anal. 73 (1987) 107-112. | MR | Zbl
,[35] 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] Counterexamples to the Baum-Connes conjecture, Geom. Funct. Anal. 12 (2) (2002) 330-354. | MR | Zbl
, , ,[37] A coarse Mayer-Vietoris principle, Math. Proc. Cambridge Philos. Soc. 114 (1993) 85-97. | MR | Zbl
, , ,[38] 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] Lectures on special Lagrangian submanifolds, AMS/IP Stud. Adv. Math. 23 (1999) 151-182. | MR | Zbl
,[40] Noncommutative geometry of tilings and gap labelling, Rev. Math. Phys. 7 (7) (1995) 1133-1180. | MR | Zbl
,[41] An irreducible unitary representation of a compact group is finite dimensional, Proc. Amer. Math. Soc. 8 (1957) 712-715. | MR | Zbl
,[42] Fell Bundles over groupoids, Proc. Amer. Math. Soc. 128 (1998) 1115-1125. | MR | Zbl
,[43] The Brauer group of a locally compact groupoid, Amer. J. Math. 120 (1998) 901-954. | MR | Zbl
, , , ,[44] Théorie de Kasparov équivariante et groupoïdes, 16 (1999) 361-390. | MR | Zbl
,[45] Gerbes over orbifolds and twisted K-theory, Comm. Math. Phys. 245 (2004) 449-489. | MR | Zbl
, ,[46] Chern character in twisted K-theory, equivariant and holomorphic cases, Comm. Math. Phys. 236 (2003) 161-186. | MR | Zbl
, ,[47] The basic gerbe over a compact simple Lie group, Enseign. Math. (2) 49 (2003) 307-333. | MR | Zbl
,[48] Gerbes, (twisted) K-theory, and the supersymmetric WZW model, hep-th/0206139.
,[49] K-theory and Ramond-Ramond charge, J. High Energy Phys. 11 (1997) 2-7. | MR | Zbl
, ,[50] 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] Functoriality of the bimodule associated to a Hilsum-Skandalis map, 18 (1999) 235-253. | MR | Zbl
,[52] 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] Introduction to the language of stacks and gerbes, math.AT/0212266.
,[54] Orbifolds, sheaves and groupoids, 12 (1997) 3-21. | MR | Zbl
, ,[55] 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] Equivalence and isomorphism for groupoid
[57] 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]
[59] Loop Groups, Oxford Mathematical Monographs, Oxford University Press, New York, 1986. | MR | Zbl
, ,
[60] Continuous trace
[61] A Groupoid Approach to
[62] Représentation des produits croisés d'algèbres de groupoïdes, J. Operator Theory 18 (1987) 67-97. | MR | Zbl
,[63] Continuous-trace algebras from the bundle theoretic point of view, J. Austral. Math. Soc. Ser. A 47 (1989) 368-381. | MR | Zbl
,
[64] A short proof that
[65] Equivariant K-theory, Inst. Hautes Études Sci. Publ. Math. 34 (1968) 129-151. | Numdam | MR | Zbl
,[66] Fredholm complexes, Quart. J. Math. Oxford Ser. (2) 21 (1970) 385-402. | MR | Zbl
,[67] The coarse Baum-Connes conjecture and groupoids, Topology 41 (4) (2002) 807-834. | MR | Zbl
, , ,[68] La conjecture de Novikov pour les feuilletages hyperboliques, 16 (1999) 129-184. | MR | Zbl
,[69] La conjecture de Baum-Connes pour les feuilletages moyennables, 17 (3) (1999) 215-264. | MR | Zbl
,[70] Central extensions and physics, J. Geom. Phys. 4 (1987) 207-258. | MR | Zbl
, ,
[71] On primitive ideal spaces of
[72] K-theory and
[73] Sur les théorèmes de De Rham, Comment. Math. Helv. 26 (1959) 119-145. | MR | Zbl
,[74] Extensions of symplectic groupoids and quantization, J. Reine Angew. Math. 417 (1991) 159-189. | MR | Zbl
, ,[75] D-branes and K-theory, J. High Energy Phys. 12 (1998) 19-44. | MR | Zbl
,[76] Overview of K-theory applied to strings, Internat. J. Modern Phys. A 16 (2001) 693-706. | MR | Zbl
,[77] Morita equivalent symplectic groupoids, Math. Sci. Res. Inst. Publ. 20 (1991) 291-311. | MR | Zbl
,- 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
- 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
- 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
- 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
- The completion theorem in twisted equivariant
-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 - Geometric
-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 - 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
- Equivariant
-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 - 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
- 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
- Twisted geometric
-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 - Twisted differential cohomology, Algebraic Geometric Topology, Volume 19 (2019) no. 4, pp. 1631-1710 | DOI:10.2140/agt.2019.19.1631 | Zbl:1447.55005
- 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
- Inverse systems of groupoids, with applications to groupoid
-algebras, Journal of Functional Analysis, Volume 276 (2019) no. 3, pp. 716-750 | DOI:10.1016/j.jfa.2018.05.013 | Zbl:1416.46054 - 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
- 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
- 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
- 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
- Notes on twisted equivariant
-theory for -algebras, International Journal of Mathematics, Volume 27 (2016) no. 6, p. 28 (Id/No 1650058) | DOI:10.1142/s0129167x16500580 | Zbl:1347.19001 - 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
- 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
- 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
- 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
-
-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 - 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 - 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
- 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
- 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
- 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
- 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
- Twisted
-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 - 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
- Twisted
-theory, -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 - Twisted equivariant matter, Annales Henri Poincaré, Volume 14 (2013) no. 8, pp. 1927-2023 | DOI:10.1007/s00023-013-0236-x | Zbl:1286.81109
- Character formulæ and GKRS multiplets in equivariant
-theory, Selecta Mathematica. New Series, Volume 19 (2013) no. 1, pp. 49-95 | DOI:10.1007/s00029-012-0102-6 | Zbl:1267.19006 - 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
- Motivic twisted
-theory, Algebraic Geometric Topology, Volume 12 (2012) no. 1, pp. 565-599 | DOI:10.2140/agt.2012.12.565 | Zbl:1282.14040 - 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
- 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
- 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
- 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
- Chern-Weil construction for twisted
-theory, Communications in Mathematical Physics, Volume 299 (2010) no. 1, pp. 225-254 | DOI:10.1007/s00220-010-1080-1 | Zbl:1204.19006 - 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
- 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
- The ring structure for equivariant twisted
-theory, Journal für die Reine und Angewandte Mathematik, Volume 635 (2009), pp. 97-148 | DOI:10.1515/crelle.2009.077 | Zbl:1180.19004 - Equivariant representable
-theory, Journal of Topology, Volume 2 (2009) no. 1, pp. 123-156 | DOI:10.1112/jtopol/jtp003 | Zbl:1163.19003 - Twisted
-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 - 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
- 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
- Stacky Lie Groups, International Mathematics Research Notices, Volume 2008 (2008) | DOI:10.1093/imrn/rnn082
- 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
- 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
- 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
- Twisted equivariant
-theory for proper actions of discrete groups, -Theory, Volume 38 (2008) no. 2, pp. 95-111 | DOI:10.1007/s10977-007-9016-z | Zbl:1141.19004 - Sheaf theory for stacks in manifolds and twisted cohomology for
-gerbes, Algebraic Geometric Topology, Volume 7 (2007), pp. 1007-1062 | DOI:10.2140/agt.2007.7.1007 | Zbl:1149.14002 - 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
- Chern character for twisted
-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 - 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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