Homotopy invariance of twisted higher signatures on manifolds with boundary
Bulletin de la Société Mathématique de France, Volume 127 (1999) no. 2, p. 307-331
@article{BSMF_1999__127_2_307_0,
     author = {Leichtnam, \'Eric and Piazza, Paolo},
     title = {Homotopy invariance of twisted higher signatures on manifolds with boundary},
     journal = {Bulletin de la Soci\'et\'e Math\'ematique de France},
     publisher = {Soci\'et\'e math\'ematique de France},
     volume = {127},
     number = {2},
     year = {1999},
     pages = {307-331},
     doi = {10.24033/bsmf.2350},
     zbl = {0945.58020},
     mrnumber = {2000f:58048},
     language = {en},
     url = {http://www.numdam.org/item/BSMF_1999__127_2_307_0}
}
Leichtnam, éric; Piazza, Paolo. Homotopy invariance of twisted higher signatures on manifolds with boundary. Bulletin de la Société Mathématique de France, Volume 127 (1999) no. 2, pp. 307-331. doi : 10.24033/bsmf.2350. http://www.numdam.org/item/BSMF_1999__127_2_307_0/

[APS1] Atiyah (M.F.), Patodi (V.), Singer (I.). - Spectral Asymmetry and Riemannian Geometry, I, Math. Proc. Cambridge Phil. Soc., t. 77, p. 43, 1975. | MR 53 #1655a | Zbl 0297.58008

[APS2] Atiyah (M.F.), Patodi (V.), Singer (I.). - Spectral Asymmetry and Riemannian Geometry, I, Math. Proc. Cambridge Phil. Soc., t. 78, p. 405, 1976. | Zbl 0314.58016

[AS] Atiyah (M.F.), Singer (I.). - The index of elliptic operators, III, Ann. Math., t. 87, 1968, p. 546. | Zbl 0164.24301

[BiCh] Bismut (J.-M.), Cheeger (J.). - Remarks on The Index Theorem for Families of Dirac Operators on Manifolds with Boundary. - Differential Geometricy, B. Lawson and K. Teneblat (eds), Longman Scientific, 1992.

[Ch1] Cheeger (J.). - On the Hodge Theory of Riemannian Pseudomanifolds, Proc. Symposia Pure Mathematics, vol. 36, p. 91, 1980. | MR 83a:58081 | Zbl 0461.58002

[Ch2] Cheeger (J.). - Spectral Geometry of Singular Riemann Spaces, J. Diff. Geom., t. 18, 1983, p. 575. | MR 85d:58083 | Zbl 0529.58034

[Co] Connes (A.). - Noncommutative geometry. - Academic Press, 1994. | MR 95j:46063 | Zbl 0818.46076

[CM] Connes (A.), Moscovici (H.). - Cyclic Cohomology, the Novikov Conjecture and Hyperbolic Groups, Topology, t. 29, 1990, p. 345. | MR 92a:58137 | Zbl 0759.58047

[FS] Fintushel (R.), Stern (R.). - Rational blowdowns of smooth 4-manifolds, J. Diff. Geom., t. 46, 1997, p. 181. | MR 98j:57047 | Zbl 0896.57022

[FRR] Ferry (S.), Ranicki (A.), Rosenberg (J.). - A history and survey of the Novikov conjecture, in Novikov Conjectures, Index Theorems and Rigidity, vol. 1, London Math. Soc., Lecture Notes Series, t. 226, 1995. | MR 97f:57036 | Zbl 0954.57018

[Ka] Karoubi (M.). - Homologie Cyclique et K-Théorie, Astérisque, t. 149, 1987. | MR 89c:18019 | Zbl 0648.18008

[HS] Hilsum (M.), Skandalis (G.). - Invariance par homotopie de la signature à coefficient dans un fibré presque plat, J. reine angew. Math., t. 423, 1992, p. 73. | MR 93b:46137 | Zbl 0731.55013

[LP1] Leichtnam (E.), Piazza (P.). - The b-pseudodifferential calculus on Galois coverings and a higher Atiyah-Patodi-Singer index theorem, Mémoires Soc. Math. France, t. 68, 1997. | Numdam | MR 99d:58168 | Zbl 0942.58003

[LP2] Leichtnam (E.), Piazza (P.). - Spectral sections and higher Atiyah-Patodi-Singer index theory on Galois coverings, GAFA, t. 8, 1996, p. 17. | MR 2000b:58043 | Zbl 0913.58055

[LP3] Leichtnam (E.), Piazza (P.). - Higher eta invariants and the Novikov conjecture on manifolds with boundary, C. R. Acad. Sciences, t. 327 serie I, 1998, p. 497-502. | MR 99j:58199 | Zbl 0920.58046

[L1] Lott (J.). - Superconnections and higher index theory, GAFA, t. 2, 1992, p. 421. | MR 93j:58128 | Zbl 0777.58038

[L2] Lott (J.). - Higher eta invariants, K-Theory, t. 6, 1992, p. 191. | MR 93j:58129 | Zbl 0773.58026

[L3] Lott (J.). Diffeomorphisms, Analytic Torsion and Non Commutative Geometry, Memoires AMS (in press), circulating as Preprint Max Planck Institute, Bonn, 1996.

[L4] Lott (J.). - The Zero-in-the-Spectrum Question, Enseign. Math., t. 42, 1996, p. 341-376. | MR 97h:58145 | Zbl 0874.58086

[Lu] Lusztig (G.). - Novikov's Higher Signature and Families of Elliptic Operators, J. Differential. Geom., t. 7, 1971, p. 229. | MR 48 #1250 | Zbl 0265.57009

[Me] Melrose (R.). - The Atiyah-Patodi-Singer Index Theorem. - A. and K. Peters, 1993. | MR 96g:58180 | Zbl 0796.58050

[MP1] Melrose (R.), Piazza (P.). - Families of Dirac operators, boundaries and the b-calculus, J. Differential. Geom., t. 46, n° 1, 1997, p. 99. | MR 99a:58144 | Zbl 0955.58020

[MP2] Melrose (R.), Piazza (P.). - An index theorem for families of Dirac operators on odd dimensional manifolds with boundary, J. Differential. Geom., t. 46, n° 2, 1997, p. 287. | MR 99a:58145 | Zbl 0920.58053

[Pi] Piazza (P.). - Dirac operators, heat kernels and microlocal analysis, Part I, Rend. Circolo Mat. Palermo, t. 49, 1997, p. 187. | Zbl 0906.58050