The $b$-pseudodifferential calculus on Galois coverings and a higher Atiyah-Patodi-Singer index theorem

The

b

-pseudodifferential calculus on Galois coverings and a higher Atiyah-Patodi-Singer index theorem

Leichtnam, Éric ; Piazza, Paolo

Mémoires de la Société Mathématique de France, no. 68 (1997) , 130 p.

MR Zbl | 3 citations dans Numdam

DOI : 10.24033/msmf.382

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     author = {Leichtnam, \'Eric and Piazza, Paolo},
     title = {The $b$-pseudodifferential calculus on {Galois} coverings and a higher {Atiyah-Patodi-Singer} index theorem},
     series = {M\'emoires de la Soci\'et\'e Math\'ematique de France},
     year = {1997},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {68},
     doi = {10.24033/msmf.382},
     mrnumber = {99d:58168},
     zbl = {0942.58003},
     language = {en},
     url = {https://www.numdam.org/item/MSMF_1997_2_68__1_0/}
}

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Leichtnam, Éric; Piazza, Paolo. The $b$-pseudodifferential calculus on Galois coverings and a higher Atiyah-Patodi-Singer index theorem. Mémoires de la Société Mathématique de France, Nouvelle série, no. 68 (1997), 130 p. doi: 10.24033/msmf.382

Bibliographie
Cité par

[A1] M.F. Atiyah, K-theory, Benjamin, 1967. | Zbl | MR

[A2] M.F. Atiyah: Elliptic operators, discrete groups and von Neumann algebras, Astérisque, 32 (1976) p.43. | Zbl | MR | Numdam

[ABP] Atiyah-Bott-Patodi: On The Heat Equation and The Index Theorem, Inv. Math. 19, (1968), p. 113. | Zbl

[APS 1,3] M.F. Atiyah-V.Patodi-I.Singer: Spectral Asymmetry and Riemannian Geometry I, III, Math. proc. Cambridge Philo. Soc. 77, (1975), p.43; 79, (1976), p.71. | Zbl

[AS 1,3] M.F. Atiyah-I.Singer: The Index of Elliptic Operators I, III, Annals of Maths, 87 (1968) p. 484; p. 546. | Zbl | MR

[BJ] S.Baaj-P.Julg: Théorie Bivariante de Kasparov et Opérateurs Non Bornés dans les C*-Modules Hilbertiens, C.R.Acad. Sci. Paris 296, Ser. I, (1883) p. 875. | Zbl

[BGV] N.Berline-E.Getzler-M.Vergne: Heat Kernels and Dirac Operators, Springer Verlag (1992). | Zbl

[BV] N.Berline-M.Vergne: The Equivariant Chern Character and Index of G-Invariant Operators, In D-modules, Representation Theory and Quantum Groups, Venezia 1992. Lecture Notes in Math. 1565, (1992). | Zbl

[B] J-M.Bismut: The Atiyah-Singer Index Theorem for Families of dirac Operators: Two Heat Equations Proofs, Inv. Math. 83, (1986) p.91. | Zbl | MR

[BC 1,2] J-M.Bismut-J.Cheeger: Families Index For Manifolds with Boundaries, Superconnections and Cones,I and II, Journ. Funct. Anal. 89 (1990), p. 313, 90 (1991), p.306. | Zbl

[BC 3] J-M.Bismut-J.Cheeger: Remarks on The Index Theorem for Families of Dirac Operators on Manifolds with Boundary, Differential Geometry, B. Lawson and K.Teneblat (eds), Longman Scientific, (1992).

[Br] Breuer: Fredholm Theories in von Neumann algebras I, II, Math. Ann. 178 (1968), p 243; 180, (1969), p 313. | Zbl | MR

[CG] J.Cheeger-M.Gromov: Bounds on the von Neumann dimension of L2-cohomology and the Gauss-Bonnet theorem on open manifolds, J. Diff. Geom. 21 (1985) p.1. | Zbl

[CGT] J.Cheeger-M.Gromov-M.Taylor: Finite Propagation Speed, Kernels Estimates for Functions of the Laplace Operator and the Geometry of Complete Riemannian Manifolds, J. Diff. Geom. 17 (1982) p. 15. | Zbl | MR

[C] A.Connes: Noncommutative geometry, Academic Press, (1994). | Zbl | MR

[CM] A.Connes-H.Moscovici: Cyclic Cohomology, The Novikov Conjecture and Hyperbolic Groups, Topology, 29 No 3, (1990) p.345. | Zbl | MR

[DZ] X.Dai-W.Zhang: Higher spectral flow, Preprint (1996).

[ES] D.Efremov-M.Shubin: Spectrum Distribution Function and variational principle for automorphic operators on hyperbolic space, Seminaire E.D.P Ecole Polytechnique (1988-1989). | Zbl | Numdam

[Ge] E.Getzler: Pseudodifferential Operators on Supermanifolds and the Atiyah-Singer Index Theorem, Comm. Math. Phys. 92 (1983) p. 163. | Zbl | MR

[G] P.Gilkey: Invariance Theory, The Heat Equation, and The Atiyah-Singer Index Theorem, Publish or Perish, (1984). | Zbl

[K] G.Kasparov: Equivariant K-Theory and the Novikov Conjecture, Inventiones Math. 91, (1988) p. 147. | Zbl | MR

[Ka] M.Karoubi: Homologie Cyclique et K-Théorie, Astérisque 149 (1987). | Zbl | MR | Numdam

[L1] J.Lott: Superconnections and higher index theory, Geom. Funct. An. 2 (1992) p.421. | Zbl | MR

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

[Lu] G.Lustzig: Novikov's Higher Signature and Families of Elliptic Operators, J.Diff. Geom 7, (1971), p. 229. | Zbl

[Me] R.Melrose: The Atiyah-Patodi-Singer Index Theorem, A. K Peters 1993. | Zbl | MR

[Me2] R.Melrose: Differential Analysis on Manifolds with Corners, in preparation.

[MeNi] R.Melrose-V.Nistor: Homology of Pseudo-differential Operators I. Manifolds with Boundary, Preprint (1996).

[MP 1] R.Melrose-P.Piazza: Family of Dirac Operators, Boundaries and the b-Calculus, J. Diff. Geom. 46 (1997) p1. | Zbl

[MP 2] R.Melrose-P.Piazza: An Index Theorem For Families of Dirac Operators on Odd-dimensional Manifolds with Boundary, J. Diff. Geom. To appear. | Zbl

[MF] A.Mishenko-A.Fomenko: The Index of Elliptic Operators over C*-Algebras, Izv. Akad. Nauk SSSR, Ser. Mat. 43, (1979) p.831. | Zbl | MR

[Pa] W.Paschke: Inner Product Modules Over B*-Algebras, Trans AMS, 182, (1973). | Zbl | MR

[P1] P.Piazza: On The Index of Elliptic Operators on Manifolds with Boundary, Journ. Funct. Anal. 117, (1993), p.308. | Zbl | MR

[Q] D.Quillen: Superconnections and the Chern Character, Topology 24 (1985) p.89. | Zbl | MR

[R] M.Ramachandran: von Neumann Index Theorems for Manifolds With Boundary, J.Diff. Geom. (1992).

[S] I.Singer: Some remarks on operator theory and index theory, Lect. Notes Math 575. | Zbl | MR

[Sh 1] M.Shubin: Spectral Theory of Elliptic pseudodifferential operators, Springer Verlag 1987.

[Sh 2] M.Shubin: L2-Riemann-Roch theorem for elliptic operators, GAFA (1995). | Zbl | MR

[Wu] F.Wu: Higher noncommutative spectral flow, Preprint (1996).

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