Elliptic operators and higher signatures
Annales de l'Institut Fourier, Volume 54 (2004) no. 5, pp. 1197-1277.

Building on the theory of elliptic operators, we give a unified treatment of the following topics: - the problem of homotopy invariance of Novikov's higher signatures on closed manifolds, - the problem of cut-and-paste invariance of Novikov's higher signatures on closed manifolds, - the problem of defining higher signatures on manifolds with boundary and proving their homotopy invariance.

En s'appuyant sur la théorie des opérateurs elliptiques, nous donnons une approche unifiée des sujets suivants : - le problème de l'invariance par homotopie des hautes signatures de Novikov des variétés compactes orientées sans bord, - le problème de l'invariance par coupure et collage des hautes signatures de Novikov des variétés compactes orientées sans bord, - le problème de définir les hautes signatures de variétés à bord et de prouver leur invariance par homotopie.

DOI: 10.5802/aif.2049
Classification: 19E20,  53C05,  58J05,  58J28
@article{AIF_2004__54_5_1197_0,
     author = {Leichtnam, \'Eric and Piazza, Paolo},
     title = {Elliptic operators and higher signatures},
     journal = {Annales de l'Institut Fourier},
     pages = {1197--1277},
     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
     volume = {54},
     number = {5},
     year = {2004},
     doi = {10.5802/aif.2049},
     zbl = {1069.58014},
     mrnumber = {2127848},
     language = {en},
     url = {http://archive.numdam.org/articles/10.5802/aif.2049/}
}
TY  - JOUR
AU  - Leichtnam, Éric
AU  - Piazza, Paolo
TI  - Elliptic operators and higher signatures
JO  - Annales de l'Institut Fourier
PY  - 2004
DA  - 2004///
SP  - 1197
EP  - 1277
VL  - 54
IS  - 5
PB  - Association des Annales de l’institut Fourier
UR  - http://archive.numdam.org/articles/10.5802/aif.2049/
UR  - https://zbmath.org/?q=an%3A1069.58014
UR  - https://www.ams.org/mathscinet-getitem?mr=2127848
UR  - https://doi.org/10.5802/aif.2049
DO  - 10.5802/aif.2049
LA  - en
ID  - AIF_2004__54_5_1197_0
ER  - 
%0 Journal Article
%A Leichtnam, Éric
%A Piazza, Paolo
%T Elliptic operators and higher signatures
%J Annales de l'Institut Fourier
%D 2004
%P 1197-1277
%V 54
%N 5
%I Association des Annales de l’institut Fourier
%U https://doi.org/10.5802/aif.2049
%R 10.5802/aif.2049
%G en
%F AIF_2004__54_5_1197_0
Leichtnam, Éric; Piazza, Paolo. Elliptic operators and higher signatures. Annales de l'Institut Fourier, Volume 54 (2004) no. 5, pp. 1197-1277. doi : 10.5802/aif.2049. http://archive.numdam.org/articles/10.5802/aif.2049/

[1] M. Atiyah, Global theory of elliptic operators, Univ. of Tokyo Press, 1970, p. 21-30 | Zbl

[2] M.F. Atiyah & R. Bott, The index theorem for manifolds with boundary, 1964, p. 175-186 | Zbl

[3] M.F. Atiyah, H. Donnelly & I.M. Singer, Eta invariants, signature defects of cusps and values of L-functions, Ann. of Math. 118 (1983) p. 131-177 | MR | Zbl

[4] M.F. Atiyah, H. Donnelly & I.M. Singer, Signature defects of cusps and values of L-functions: the non-split case., Ann. of Math 119 (1984) p. 635-637 | MR | Zbl

[5] M.F. Atiyah, V.K. Patodi & I.M. Singer, Spectral asymmetry and Riemannian geometry. I, Math. Proc. Camb. Phil. Soc 77 (1975) p. 43-69 | MR | Zbl

[6] M.F. Atiyah, V.K. Patodi & I.M. Singer, Spectral asymmetry and Riemannian geometry. II, Math. Proc. Camb. Phil. Soc 78 (1975) p. 405-432 | MR | Zbl

[7] M.F. Atiyah, V.K. Patodi & I.M. Singer, Spectral asymmetry and Riemannian geometry. III, Math. Proc. Camb. Phil. Soc 79 (1976) p. 71-99 | MR | Zbl

[8] M. Atiyah & I. Singer, The index of elliptic operators. IV., Annals of Math. (2) 93 (1971) p. 119-138 | MR | Zbl

[9] M. Atiyah & I. Singer, Index theory of skew-adjoint Fredholm operators, Inst. Hautes Études Sci. Publ. Math 37 (1969) p. 305-326 | Numdam | MR | Zbl

[10] P. Baum & A. Connes, Leafwise homotopy equivalence and rational Pontrjagin classes, Foliations, Advances Studies in Pure Math. 5, North-Holland, 1985, p. 1-14 | Zbl

[11] P. Baum, A. Connes & N. Higson, Classifying Space for proper actions and K-Theory of group C * -algebras, Contemporary Mathematics 167 (1994) p. 241-291 | MR | Zbl

[12] P. Baum & R. Douglas, K homology and index theory, Proc. Sympos. Pure Math. Soc. 38, Amer. Math. Soc., 1982, p. 117-173 | Zbl

[13] N. Berline, E. Getzler & M. Vergne, Heat kernels and Dirac operators, 298, Springer Verlag, 1992 | MR | Zbl

[14] J.-M. Bismut, The Atiyah-Singer index theorem for families of Dirac operators: two heat-equation proofs, Inv. Math 83 (1986) p. 91-151 | MR | Zbl

[15] J.-M. Bismut & J. Cheeger, η-Invariants and their adiabatic limits, Jour. of the Amer. Math. Soc 2 (1989) p. 33-70 | MR | Zbl

[16] J.-M. Bismut & J. Cheeger, Families index for manifolds with boundary, superconnections and cones I, Jour. Funct. Anal. 89 (1990) p. 313-363 | MR | Zbl

[17] J.-M. Bismut & D.S. Freed, The analysis of elliptic families: Metrics and connections on determinant bundles, Comm. Math. Phys 106 (1986) p. 159-176 | MR | Zbl

[18] J.-M. Bismut & D.S. Freed, The analysis of elliptic families: Dirac operators, eta invariants and the holonomy theorem of Witten, Comm. Math. Phys. 107 (1986) p. 103-163 | MR | Zbl

[19] B. Booss-Bavnbek & K. Wojciechowski, Elliptic boundary problems for Dirac operators, Mathematics : theory and applications, Birkhäuser, 1993 | Zbl

[20] L. Boutet De Monvel, Boundary problems for pseudodifferential operators, Acta Math. 126 (1971) p. 11-51 | MR | Zbl

[21] P. Brown, R. Douglas & P. Fillmore, Unitary equivalence modulo the compact operators and extensions of C * -algebras, Lecture Notes in Math 345, Springer Verlag, 1973, p. 58-128 | Zbl

[22] J. Brüning & R. Seeley, An index theorem for first order regular singular operators, Amer. J. Math 110 (1988) p. 659-714 | MR | Zbl

[23] U. Bunke, On the gluing problem for the η-invariant, Journal of Differential Geometry 41 (1995) p. 397-448 | MR | Zbl

[24] J. Cheeger, On the spectral geometry of spaces with cone-like singularities, Proc. Nat. Acad. Sci. U.S.A 76 (1979) no.5 p. 2103-2106 | MR | Zbl

[25] J. Cheeger, Spectral geometry of singular Riemann spaces, J. Differential Geom. 18 (1983) p. 575-657 | MR | Zbl

[26] A. Chou, The Dirac operator on spaces with conical singularities and positive scalar curvatures, Trans. Amer. Math. Soc. 289 (1985) no.1 p. 1-40 | MR | Zbl

[27] A. Connes, Noncommutative Geometry. Part I: The Chern character in K-Homology. Part II de Rham homology and noncommutative algebras., Preprint I.H.E.S, 1983

[28] A. Connes, Noncommutative Geometry, Academic Press, 1994 | MR | Zbl

[29] A. Connes & H. Moscovici, Cyclic cohomology, the Novikov conjecture and hyperbolic groups, Topology 29 (1990) p. 345-388 | MR | Zbl

[30] A. Connes, M. Gromov & H. Moscovici, Conjecture de Novikov et fibrés presque plats, C.R. Acad. Sci. Paris Sér. I Math 310 (1990) no.5 p. 273-277 | MR | Zbl

[31] A. Connes, M. Gromov & H. Moscovici, Group cohomology with Lipschitz control and higher signatures, Geom. Funct. Anal 3 (1993) no.1 p. 1-78 | MR | Zbl

[32] J. Cuntz, Noncommutative simplicial complexes and the Baum-Connes conjecture, Geom. Funct. Anal 12 (2002) no.2 p. 307-329 | MR | Zbl

[33] X. Dai & W. Zhang, Splitting the family index, Comm. Math. Phys 182 (1996) p. 303-318 | MR | Zbl

[34] X. Dai & W. Zhang, Higher spectral flow, Journal of Funct. Analysis 157 (1998) p. 432-469 | MR | Zbl

[35] X. Dai & W. Zhang, Real embeddings and the Atiyah-Patodi-Singer index theorem for Dirac operators, Loo-Keng Hua: a great mathematician of the twentieth century, Asian J. Math 4 (2000) no.4 p. 775-794 | MR | Zbl

[36] M. Farber & S. Weinberger, On the zero-in-the-spectrum conjecture, Ann. of Math. (2) 154 (2001) no.1 p. 139-154 | MR | Zbl

[37] S. Ferry, A. Ranicki & J. Rosenberg, A history and survey of the Novikov conjecture., Lecture Note Ser. 226, Cambridge Univ. Press, 1995, p. 7-66 | Zbl

[38] E. Getzler, Pseudodifferential operators on supermanifolds and the Atiyah-Singer index theorem, Comm. Math. Phys 92 (1983) no.2 p. 163-178 | MR | Zbl

[39] E. Ghys, Les groupes hyperboliques, Astérisque 189-190, 1990, p. 203-238 | Numdam | Zbl

[40] E. Ghys & P. De La Harpe, Hyperbolic groups in the theory of Mikhael Gromov, Birkhäuser, 1990

[41] D. Grieser, Basics of the b-calculus, Oper. Theory Adv. Appl 125, Birkhäuser, 1999, p. 30-84 | Zbl

[42] A. Gorokhovsky & J. Lott, Local index theory over etale groupoids, J. Reine angew. Math 560 (2003) p. 151-198 | MR | Zbl

[43] M. Gromov, Hyperbolic groups, Math. Sci. Res. Inst. Publ 8, Springer, 1987, p. 75-263 | Zbl

[44] M. Gromov, Positive curvature, macroscopic dimension, spectral gaps and higher signatures, Progress in Mathematics, Birkäuser, 1995 | Zbl

[45] M. Gromov & M. Shubin, Von Neumann spectra near zero, Geom. Funct. Anal 1 (1991) no.4 p. 375-404 | MR | Zbl

[46] E. Guentner, N. Higson & S. Weinberger, The Novikov Conjecture for linear groups, Preprint, 2003 | Numdam | Zbl

[47] N. Higson, A Primer in KK-Theory, Proc. Sympos. Pure Math. 51, 1990, p. 239-283 | Zbl

[48] N. Higson & G. Kasparov, Operator K-theory for groups which act properly and isometrically on Hilbert space, Electron. Res. Announc. Amer. Math. Soc 3 (1997) p. 131-142 | MR | Zbl

[49] N. Higson & G. Kasparov, E-theory and KK-theory for groups which act properly and isometrically on Hilbert space, Invent. Math. 144 (2001) no.1 p. 23-74 | MR | Zbl

[50] N. Higson & J. Roe, John Analytic K-homology, Oxford University Press, Oxford Mathematical Monographs, Oxford Science Publications, 2000 | MR | Zbl

[51] N. Higson, J. Roe & T. Schick, Spaces with vanishing l 2 -homology and their fundamental groups (after Farber and Weinberger), Geom. Dedicata 87 (2001) no.1-3 p. 335-343 | MR | Zbl

[52] M. Hilsum, Index classes of Hilbert modules with boundary, Preprint Paris 6, March 2001 | MR

[53] M. Hilsum & G. Skandalis, Invariance de la signature à coefficients dans un fibré presque plat, J. Reine Angew. math 423 (1990) p. 73-99 | MR | Zbl

[54] M. Hirsch, Differential topology, Graduate texts in mathematics 33, Springer-Verlag, 1976 | Zbl

[55] F. Hirzebruch, The signature theorem: reminiscences and recreation, Ann. of Math. Studies 70, Princeton Univ. Press, 1970, p. 3-31 | Zbl

[56] R. Ji, Smooth dense subalgebras of reduced group C * -algebras, Schwartz cohomology of groups, and cyclic cohomology, J. Funct. Anal. 107 (1992) no.1 p. 1-33 | MR | Zbl

[57] M. Joachim & T. Schick, Positive and negative results concerning the Gromov-Lawson-Rosenberg conjecture, Contemp. Math 258, Amer. Math. Soc., 2000, p. 213-226 | Zbl

[58] P. Jolissaint, Rapidly decreasing functions in reduced C * -algebras of groups, Trans. Amer. Math. Soc 317 (1990) no.1 p. 167-196 | MR | Zbl

[59] M. Karoubi, Homologie cyclique et K-théorie, Astérisque 149 (1987) | MR | Zbl

[60] J. Kaminker & J. Miller, Homotopy invariance of the analytic index of signature operators over C * -algebras, J. Operator Theory 14 (1985) p. 113-127 | MR | Zbl

[61] U. Karras, M. Kreck, W. Neumann & E. Ossa, Cutting and pasting of manifolds; SK-groups, Publish or Perish, 1973 | MR | Zbl

[62] G. Kasparov, Topological invariants of elliptic operators K-homology (Russian), Math. USSR-Izv 9 (1975) no.4 p. 751-792 | MR | Zbl

[64] G. Kasparov, Equivariant KK-theory and the Novikov conjecture, Invent. Math 91 (1988) no.1 p. 147-201 | MR | Zbl

[65] G. Kasparov, Novikov’s conjecture on higher signatures: The operator K-theory approach, Contemporary Math 145 (1993) p. 79-99 | Zbl

[66] G. Kasparov & G. Skandalis, Groups acting on buildings, operator K-theory, and Novikov’s conjecture, K-Theory 4 (1991) no.4 p. 303-337 | MR | Zbl

[67] G. Kasparov & G. Skandalis, Groups acting properly on bolic spaces and the Novikov conjecture, Ann. of Math 158 (2003) p. 165-206 | MR | Zbl

[68] N. Keswani, Geometric K-homology and controlled paths, New York J. Math 5 (1999) p. 53-81 | MR | Zbl

[69] V. Lafforgue, K-théorie bivariante pour les algèbres de Banach et conjecture de Baum-Connes, Invent. Math 149 (2002) no.1 p. 1-95 | MR | Zbl

[70] M. Lesch, Operators of Fuchs type, conical singularities, and asymptotic methods, Teubner-Texte zur Mathematik 136, B. G. Teubner Verlagsgesellschaft mbH, 1997 | Zbl

[71] B. Lawson & M-L. Michelsohn, Spin Geometry, Princeton mathematical series 38, Princeton University Press, 1989 | MR | Zbl

[72] E. Leichtnam, J. Lott & P. Piazza, On the homotopy invariance of higher signatures for manifolds with boundary, Journal of Differential Geometry 54 (2000) p. 561-633 | MR | Zbl

[73] E. Leichtnam, W. Lück & M. Kreck, On the cut-and-paste property of higher signatures on a closed oriented manifold, Topology 41 (2002) p. 725-744 | MR | Zbl

[74] E. Leichtnam & P. Piazza, The b-pseudo-differential calculus on Galois coverings and a higher Atiyah-Patodi-Singer index theorem, Mémoires de la Société Mathématiques de France 68 (1997) | Numdam | Zbl

[75] E. Leichtnam & P. Piazza, Spectral sections and higher Atiyah-Patodi-Singer index theory on Galois coverings, GAFA 8 (1998) p. 17-58 | MR | Zbl

[76] E. Leichtnam & P. Piazza, A Higher Atiyah-Patodi-Singer Index theorem for the signature operator on Galois Coverings, Annals of Global Analysis and Geometry 18 (2000) p. 171-189 | MR | Zbl

[77] E. Leichtnam & P. Piazza, Homotopy invariance of twisted higher signatures on manifolds with boundary, Bull. Soc. Math. France 127 (1999) p. 307-331 | Numdam | MR | Zbl

[78] E. Leichtnam & P. Piazza, On higher eta invariants and metrics of positive scalar curvature, K-Theory 24 (2001) p. 341-359 | MR | Zbl

[79] E. Leichtnam & P. Piazza, Dirac index classes and the noncommutative spectral flow, Jour. Funct. Anal 200 (2003) p. 348-400 | MR | Zbl

[80] E. Leichtnam & P. Piazza, Etale Groupoids, eta invariants and index theory, e-print. To appear in J. Reine Angew. Math, math.DG/0308184, August 2003 | Zbl

[81] E. Leichtnam & P. Piazza, Cut-and-Paste on Foliated Bundles, e-print. To appear in the Contemporary Mathematics. Volume Spectral Geometry of Manifolds with boundary (ed. B. Booss-Bavnbek, G. Grubb, K. Wojciechowski), math.DG/0407401, July 2004 | MR | Zbl

[82] J. Lott, Superconnections and higher index theory, GAFA 2 p. 421-454 | MR | Zbl

[83] J. Lott, Higher eta invariants, K-Theory 6 (1992) p. 191-233 | MR | Zbl

[84] J. Lott, Diffeomorphisms and noncommutative analytic torsion, Memoirs American Math. Soc 141 (1999) | MR | Zbl

[85] J. Lott, The zero-in-the-spectrum question, Enseign. Math (2) 42 (1996) no.3-4 p. 341-376 | MR | Zbl

[86] J. Lott, Signatures and higher signatures on S 1 -quotients, Math. Annalen 316 (2000) p. 617-657 | MR | Zbl

[87] J. Lott & W. Lück, L 2 -topological invariants of 3-manifolds, Inventiones Math 120 p. 15-60 | MR | Zbl

[88] W. Lueck & H. Reich, The Baum-Connes and the Farrell-Jones Conjectures in K- and L-Theory, To appear in K-Theory handbook | Zbl

[89] G. Lusztig, Novikov's higher signature and families of elliptic operators, J. Differential Geometry 7 (1972) p. 229-256 | MR | Zbl

[90] V. Mathai, The Novikov conjecture for low degree cohomology classes, Geometriae Dedicata 99 (2003) p. 1-15 | MR | Zbl

[91] R. Mazzeo & P. Piazza, Dirac operators, heat kernels and microlocal analysis. II: Analytic surgery., Rend. Mat. Appl. (7) 18 (1998) no.2 p. 221-288 | MR | Zbl

[92] R. Melrose, The Atiyah-Patodi-Singer index theorem, Research Notes in Mathematics 4, A.K. Peters, 1993 | MR | Zbl

[93] R. Melrose & V. Nistor, Homology of pseudodifferential operators I (manifolds with boundary), to appear in Amer. J. Math, 2003

[94] R. Melrose & P. Piazza, Families of Dirac operators, boundaries and the b-calculus, Journal of Differential Geometry 46 (1997) p. 99-180 | MR | Zbl

[95] R. Melrose & P. Piazza, An index theorem for families of Dirac operators on odd-dimensional manifolds with boundary, Journal of Differential Geometry 46 (1997) p. 287-334 | MR | Zbl

[96] J. Milnor & J. Stasheff, Characteristic Classes, Annals of Math. Studies 76 (1974) | MR | Zbl

[97] I. Mineyev & G. Yu, The Baum-Connes conjecture for hyperbolic groups, Invent. Math (2002) p. 97-122 | MR | Zbl

[98] A. Mishchenko, Homotopy invariants of non-simply connected manifolds. I: Rational Invariants, Math. USSR-Izvestija 4 (1970) p. 509-519 | Zbl

[99] A. Mishchenko, C * -algebras and K-theory, Lecture notes in Math 763, Springer, 1979, p. 262-274 | Zbl

[100] A. Mishchenko & A. Fomenko, The index of elliptic operators over C * -algebras (Russian), Izv. Akad. Nauk SSSR Ser. Mat 43 (1979) no.4 p. 831-859 | MR | Zbl

[101] W. Müller, Signature defects of cusps of Hilbert modular varieties and values of L-series at s=1, J. Diff. Geometry 20 (1984) p. 55-119 | MR | Zbl

[102] W. Müller, L 2 -index theory, eta invariants and values of L-functions, Contemporary Mathematics 105 (1990) p. 145-187 | Zbl

[103] W. Neumann, Manifold cutting and pasting groups, Topology 14 (1975) p. 237-244 | MR | Zbl

[104] C. Ogle, Assembly maps, K-theory, and hyperbolic groups, K-Theory 6 (1992) no.3 p. 235-265 | MR | Zbl

[105] P. Piazza, On the index of elliptic operators on manifolds with boundary, J. Funct. Anal 117 (1993) no.2 p. 308-359 | MR | Zbl

[106] P. Piazza & T. Schick, Bordism, rho-invariants and the Baum-Connes conjecture, e-print, math.KT/0407388, July 2004

[107] D. Quillen, Superconnections and the Chern character, Topology 24 (1985) p. 89-95 | MR | Zbl

[108] M. Ramachandran, Von Neumann index theorems for manifolds with boundary, Journal of Differential Geometry 38 (1993) no.2 p. 315-349 | MR | Zbl

[109] A. Ranicki, Exact sequences in the algebraic theory of surgery, Princeton University Press, 1981 | MR | Zbl

[110] J. Rosenberg, C * -algebras, positive scalar curvature and the Novikov conjecture, Publ. Math. IHES 58 (1983) p. 197-212 | Numdam | MR | Zbl

[111] J. Rosenberg, C * -algebras, positive scalar curvature and the Novikov conjecture II, Pitman Res. Notes Math 123, 1986, p. 342-374 | Zbl

[112] J. Rosenberg, C * -algebras, positive scalar curvature and the Novikov conjecture III, Topology 25 (1986) p. 319-336 | MR | Zbl

[113] T. Schick, Operator algebra and Topology, ICTP Lect. Notes Volume 9, 2002, p. 571-660 | Zbl

[114] T. Schick, Index, KK and connections, Preprint, 2003

[115] Ju. P. Solov'Ev, Discrete subgroups, Bruhat-Tits buildings and homotopy invariance of higher signatures (Russian), Uspehi Mat. Nauk 31 (1976) no.1(187) p. 261-262 | MR | Zbl

[116] Yu. P. Solovyov & E.V. Troitsky, C * -algebras and elliptic operators in differential topology. Translated from the 1996 Russian original by Troitsky., Mathematical Monographs 192, American Mathematical Society, 2001 | Zbl

[117] S. Stolz, Positive Scalar Curvature Metrics. Existence and Classification Questions, Birkhäuser Verlag, 1994 | Zbl

[118] B. Tsygan, Homology of matrix Lie algebras over rings and Hochschild homology, Russian Math. Surv 38 (1983) no.2 p. 198-199 | MR | Zbl

[119] A. Valette, Introduction to the Baum-Connes conjecture. From notes taken by Indira Chatterji. With an appendix by Guido Mislin., Lectures in Mathematics ETH Zürich., Birkhäuser Verlag, 2002 | MR | Zbl

[120] N. Wegge-Olsen, K-Theory and C * -algebras, Oxford University Press, 1993 | MR | Zbl

[121] S. Weinberger, Aspects of the Novikov conjecture., Contemp. Math. 105, Amer. Math. Soc., 1990, p. 281-297 | Zbl

[122] S. Weinberger, Higher ρ-invariants, Contemporary Mathematics 231, 1999 | Zbl

[123] G. Yu, The coarse Baum-Connes conjecture for spaces which admit a uniform embedding into Hilbert space, Invent. Math 139 (2000) no.1 p. 201-240 | MR | Zbl

[124] F. Wu, The noncommutative spectral flow, unpublished preprint, 1997

[125] F. Wu, The Higher Γ-index for coverings of manifolds with boundaries, Fields Institute Communications 17 (1997) p. 169-183 | MR | Zbl

[<L>16</L>] J.-M. Bismut & J. Cheeger, Families index for manifolds with boundary, superconnections and cones. II, J. Funct. Anal. 90 (1990) no.2 p. 306-354 | MR | Zbl

[<L>27</L>] A. Connes, Noncommutative geometry. Part I: the Chern character in K-homology. Part II: de Rham homology and noncommutative algebras, Publications I.H.E.S. 62 (1985) p. 257-360 | MR

[<L>62</L>] G. Kasparov, Topological invariants of elliptic operators K-homology, Izv. Akad. Nauk SSSR Ser. Mat. 39 (1975) no.4 p. 796-838 | MR | Zbl

[63] G. Kasparov, K-Theory, group C * -algebras and higher signatures (Conspectus), London Math. Soc. Lecture Note Ser. 226, Cambridge Univ. Press, 1995, p. 101-146 | Zbl

[<L>98</L>] A. Mishchenko, Homotopy invariants of non-simply connected manifolds. I: Rational Invariants, Math. USSR Izv. 15 (1980) p. 87-112 | Zbl

[<L>115</L>] Ju. P. Solov'Ev, Discrete subgroups, Bruhat-Tits buildings and homotopy invariance of higher signatures (English translation), Russian Math. Survey 31 (1976) no.1 | MR | Zbl

Cited by Sources: