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On the homotopy invariance of higher signatures for manifolds with boundary
Eric Leichtnam, John Lott, and Paolo Piazza
Source: J. Differential Geom. Volume 54, Number 3
(2000), 561-633.
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Permanent link to this document: http://projecteuclid.org/euclid.jdg/1214339793
Mathematical Reviews number (MathSciNet): MR1823315
Zentralblatt MATH identifier: 1032.58012
References
[1] M. F. Atiyah, V. Patodi and I. Singer, Spectral asymmetry and Riemannian geometry. I, Math. Proc. Cambridge Phil. Soc. 77 (1975) 43-69.
Zentralblatt MATH: 0297.58008
Mathematical Reviews (MathSciNet): MR397797
Digital Object Identifier: doi:10.1017/S0305004100049410
[2] S. Baaj and P. Julg, Théorie bivariante de Kasparov et opérateurs non bornés dans les C -modules hilbertiens, C. R. Acad. Se. Paris 296 (1983) 875-878.
Zentralblatt MATH: 0551.46041
Mathematical Reviews (MathSciNet): MR715325
[3] J.-M. Bismut and J. Cheeger, Families index for manifolds with boundaries, superconnections and cones. I, J. Funct. Anal. 89 (1990) 313-363.
Zentralblatt MATH: 0696.53021
Mathematical Reviews (MathSciNet): MR1042214
Digital Object Identifier: doi:10.1016/0022-1236(90)90098-6
[4] J.-M. Bismut and D. Freed, The analysis of elliptic families. II. Dirac operators, eta invariants and the holonomy theorem, Comm. Math. Phys. 107 (1986) 103-163.
Zentralblatt MATH: 0657.58038
Mathematical Reviews (MathSciNet): MR861886
Digital Object Identifier: doi:10.1007/BF01206955
Project Euclid: euclid.cmp/1104115934
[5] J. Bruning and R. Seeley, An index theorem for first order regular singular operators, Amer. J. Math. 110, (1988) 659-714.
Zentralblatt MATH: 0664.58035
Mathematical Reviews (MathSciNet): MR955293
Digital Object Identifier: doi:10.2307/2374646
JSTOR: links.jstor.org
[6] U. Bunke, On the gluing problem for the -q-invariant, J. Differential Geom. 41 (1995) 397-448.
Zentralblatt MATH: 0821.58037
Mathematical Reviews (MathSciNet): MR1331973
Project Euclid: euclid.jdg/1214456222
[7] U. Bunke, A K-theoretic relative index theorem and Callias-type Dirac operators, Math. Ann. 303 (1995) 241-279.
Zentralblatt MATH: 0835.58035
Mathematical Reviews (MathSciNet): MR1348799
Digital Object Identifier: doi:10.1007/BF01460989
[8] J. Cheeger, Spectral geometry of singular Riemann spaces, J. Differential Geom. 18 (1983) 575-657.
Zentralblatt MATH: 0529.58034
Mathematical Reviews (MathSciNet): MR730920
Project Euclid: euclid.jdg/1214438175
[9] A. Connes, Noncommutative geometry, Academic Press. San Diego, 1994.
Zentralblatt MATH: 0818.46076
Mathematical Reviews (MathSciNet): MR1303779
[10] A. Connes and H. Moscovici, Cyclic cohomology, the Novikov Conjecture and hyperbolic groups, Topology 29 (1990) 345-388.
Zentralblatt MATH: 0759.58047
Mathematical Reviews (MathSciNet): MR1066176
Digital Object Identifier: doi:10.1016/0040-9383(90)90003-3
[11] P. de la Harpe, Groupes hyperboliques, algebres d'opérateur et un théorème de Jolissaint, C. R. Acad. Sci. Paris, Sér. I Math. 327 (1988) 771-774.
Zentralblatt MATH: 0653.46059
[12] J. Dodziuk, De Rham-Hodge theory for L2-cohomology of infinite coverings, Topology 16 (1977) 157-165.
Zentralblatt MATH: 0348.58001
Mathematical Reviews (MathSciNet): MR445560
Digital Object Identifier: doi:10.1016/0040-9383(77)90013-1
[13] H. Donnelly, The differential form spectrum of hyperbolic space, Manuscripta Math. 33 (1980) 365-385.
Zentralblatt MATH: 0464.58020
Mathematical Reviews (MathSciNet): MR612619
Digital Object Identifier: doi:10.1007/BF01798234
[14] E. Getzler, The odd Chern character in cyclic homology and spectral flow, Topology 32 (1993) 489-507.
Zentralblatt MATH: 0801.46088
Mathematical Reviews (MathSciNet): MR1231957
Digital Object Identifier: doi:10.1016/0040-9383(93)90002-D
[15] M. Hilsum, Fonctorialié en K-Théorie bivariante pour les variétés lipschitziennes, K-Theory 3 (1989) 401-440.
Zentralblatt MATH: 0702.57008
Mathematical Reviews (MathSciNet): MR1050489
Digital Object Identifier: doi:10.1007/BF00534136
[16] M. Hilsum and G. Skandalis, Invariance par homotopie de la signature à coefficients dans un fibre presque plat, J. Reine Angew. Math. 423 (1990) 73-99.
Zentralblatt MATH: 0731.55013
Mathematical Reviews (MathSciNet): MR1142484
Digital Object Identifier: doi:10.1515/crll.1992.423.73
[17] R. Ji, Smooth dense subalgebras of reduced group C* -algebras, Schwartz cohomology of groups and cyclic cohomology, J. Funct. Anal. 107 (1992) 1-33.
Zentralblatt MATH: 0787.46043
Mathematical Reviews (MathSciNet): MR1165864
Digital Object Identifier: doi:10.1016/0022-1236(92)90098-4
[18] M. Karoubi, Homologie cyclique et K-théorie, Astérisque 149 (1987).
Zentralblatt MATH: 0648.18008
Mathematical Reviews (MathSciNet): MR913964
[19] U. Karras, M. Kreck, W. Neumann and E. Ossa, Cutting and pasting of manifolds; SK-groups, Publish or Perish. Boston, 1973.
Zentralblatt MATH: 0258.57010
Mathematical Reviews (MathSciNet): MR362360
[20] J. Kaminker and J. Miller, Homotopy invariance of the analytic index of signature operators over C* -algebras, J. Operator Theory 14 (1985) 113-127.
Zentralblatt MATH: 0614.46062
Mathematical Reviews (MathSciNet): MR789380
[21] G. Kasparov, Hilbert C* -modules: theorems of Stinespring and Voiculescu, J. Operator Theory 4 (1980) 133-150.
Zentralblatt MATH: 0456.46059
Mathematical Reviews (MathSciNet): MR587371
[22] E. Leichtnam and P. Piazza, The b-pseudodifferential calculus on Galois coverings and a higher Atiyah-Patodi-Singer index theorem, Mem. Soc. Math. Fr. 68 (1997).
Zentralblatt MATH: 0942.58003
Mathematical Reviews (MathSciNet): MR1488084
[23] E. Leichtnam and P. Piazza, Spectral sections and higher Atiyah-Patodi-Singer index theory on Galois coverings, Geom. Anal, and Funct. Anal. 8 (1996) 17-58.
Zentralblatt MATH: 0913.58055
Mathematical Reviews (MathSciNet): MR1601842
Digital Object Identifier: doi:10.1007/s000390050047
[24] E. Leichtnam and P. Piazza, Homotopy invariance of twisted higher signatures on manifolds with boundary, Bull. Soc. Math. France 127 (1999) 307-331.
Zentralblatt MATH: 0945.58020
Mathematical Reviews (MathSciNet): MR1708639
[25] E. Leichtnam and P. Piazza, A higher APS index theorem for the signature operator on Galois coverings, Ann. Glob. Anal, and Geom. 18 (2000) 171-189.
Zentralblatt MATH: 0957.58017
Mathematical Reviews (MathSciNet): MR1744589
Digital Object Identifier: doi:10.1023/A:1006649505610
[26] J. Lott, Superconnections and higher index theory, Geom. Anal, and Funct. Anal.2 (1992) 421-454.
Zentralblatt MATH: 0777.58038
Mathematical Reviews (MathSciNet): MR1191568
Digital Object Identifier: doi:10.1007/BF01896662
[27] J. Lott, Higher eta invariants, K-Theory 6 (1992) 191-233.
Zentralblatt MATH: 0773.58026
Mathematical Reviews (MathSciNet): MR1189276
Digital Object Identifier: doi:10.1007/BF00961464
[28] J. Lott, The zero-in-the-spectrum question, Enseign. Math. 42 (1996) 341-376.
Zentralblatt MATH: 0874.58086
Mathematical Reviews (MathSciNet): MR1426443
[29] J. Lott, Diffeomorphisms, analytic torsion and noncommutative geometry, Mem.of the Amer. Math. Soc. 141, No. 673. (1999) viii + 56 pp.
Zentralblatt MATH: 0942.58002
Mathematical Reviews (MathSciNet): MR1618772
[30] J. Lott, Signatures and higher signatures of S1-- quotients, Math. Ann. 316 (2000) 617-657.
Zentralblatt MATH: 0946.57030
Mathematical Reviews (MathSciNet): MR1758446
Digital Object Identifier: doi:10.1007/s002080050347
[31] J. Lott and W. Luck, L2-topological invariants of 3-manifolds, Invent. Math. 120 (1995) 15-60.
Zentralblatt MATH: 0876.57050
Mathematical Reviews (MathSciNet): MR1323981
Digital Object Identifier: doi:10.1007/BF01241121
[32] G. Lusztig, Novikov's higher signature and families of elliptic operators, J. Differential Geom. 7 (1971) 229-256.
Zentralblatt MATH: 0265.57009
Mathematical Reviews (MathSciNet): MR322889
Project Euclid: euclid.jdg/1214430829
[33] R. Melrose, The Atiyah-Patodi-Singer index theorem, A. and K. Peters. Wellesley, MA, 1993.
Zentralblatt MATH: 0796.58050
Mathematical Reviews (MathSciNet): MR1348401
[34] R. Melrose and P. Piazza, Families of Dirac operators, boundaries and the b-calculus, J. Differential Geom. 46 (1997) 99-180.
Zentralblatt MATH: 0955.58020
Mathematical Reviews (MathSciNet): MR1472895
Project Euclid: euclid.jdg/1214459899
[35] R. Melrose and P. Piazza, An index theorem for families of Dirac operators on odd dimensional manifolds with boundary, J. Differential Geom. 46 (1997) 287-334.
Zentralblatt MATH: 0920.58053
Mathematical Reviews (MathSciNet): MR1484046
Project Euclid: euclid.jdg/1214459934
[37] W. Neumann, Manifold cutting and pasting groups, Topology 14 (1975) 237-244.
Zentralblatt MATH: 0311.57007
Mathematical Reviews (MathSciNet): MR380837
Digital Object Identifier: doi:10.1016/0040-9383(75)90004-X
[39] J. Rosenberg and S. Weinberger, Higher G-signatures for Lipschitz manifolds, K- Theory 7 (1993) 101-132.
Zentralblatt MATH: 0791.58004
Mathematical Reviews (MathSciNet): MR1235284
Digital Object Identifier: doi:10.1007/BF00962083
[40] N. Wegge-Olsen, K-Theory and C*-algebras, Oxford University Press, New York, 1993.
Mathematical Reviews (MathSciNet): MR1222415
Zentralblatt MATH: 0780.46038
[41] H. Whitney, Geometric integration theory, Princeton University Press, Princeton, N.J, 1957.
Zentralblatt MATH: 0083.28204
Mathematical Reviews (MathSciNet): MR87148
[42] F. Wu, The higher T-index for coverings of manifolds with boundaries, Fields Inst.Commun. 17 (1997) Cyclic cohomology and noncommutative geometry, 169-183.
Zentralblatt MATH: 0896.58062
Mathematical Reviews (MathSciNet): MR1478709
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