@book{MSMF_1997_2_68__1_0, 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}, publisher = {Soci\'et\'e math\'ematique de France}, number = {68}, year = {1997}, doi = {10.24033/msmf.382}, mrnumber = {99d:58168}, zbl = {0942.58003}, language = {en}, url = {http://archive.numdam.org/item/MSMF_1997_2_68__1_0/} }
TY - BOOK AU - Leichtnam, Éric AU - Piazza, Paolo TI - The $b$-pseudodifferential calculus on Galois coverings and a higher Atiyah-Patodi-Singer index theorem T3 - Mémoires de la Société Mathématique de France PY - 1997 IS - 68 PB - Société mathématique de France UR - http://archive.numdam.org/item/MSMF_1997_2_68__1_0/ DO - 10.24033/msmf.382 LA - en ID - MSMF_1997_2_68__1_0 ER -
%0 Book %A Leichtnam, Éric %A Piazza, Paolo %T The $b$-pseudodifferential calculus on Galois coverings and a higher Atiyah-Patodi-Singer index theorem %S Mémoires de la Société Mathématique de France %D 1997 %N 68 %I Société mathématique de France %U http://archive.numdam.org/item/MSMF_1997_2_68__1_0/ %R 10.24033/msmf.382 %G en %F MSMF_1997_2_68__1_0
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, Serie 2, no. 68 (1997), 130 p. doi : 10.24033/msmf.382. http://numdam.org/item/MSMF_1997_2_68__1_0/
[A1] K-theory, Benjamin, 1967. | Zbl | MR
,[A2] Elliptic operators, discrete groups and von Neumann algebras, Astérisque, 32 (1976) p.43. | Zbl | MR
:[ABP] On The Heat Equation and The Index Theorem, Inv. Math. 19, (1968), p. 113. | Zbl
:[APS 1,3] Spectral Asymmetry and Riemannian Geometry I, III, Math. proc. Cambridge Philo. Soc. 77, (1975), p.43; 79, (1976), p.71. | Zbl
:[AS 1,3] The Index of Elliptic Operators I, III, Annals of Maths, 87 (1968) p. 484; p. 546. | Zbl | MR
:[BJ] 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] Heat Kernels and Dirac Operators, Springer Verlag (1992). | Zbl
:[BV] 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] 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] 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] 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] Fredholm Theories in von Neumann algebras I, II, Math. Ann. 178 (1968), p 243; 180, (1969), p 313. | Zbl | MR
:[CG] 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] 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] Noncommutative geometry, Academic Press, (1994). | Zbl | MR
:[CM] Cyclic Cohomology, The Novikov Conjecture and Hyperbolic Groups, Topology, 29 No 3, (1990) p.345. | Zbl | MR
:[DZ] Higher spectral flow, Preprint (1996).
:[ES] Spectrum Distribution Function and variational principle for automorphic operators on hyperbolic space, Seminaire E.D.P Ecole Polytechnique (1988-1989). | Zbl | Numdam
:[Ge] Pseudodifferential Operators on Supermanifolds and the Atiyah-Singer Index Theorem, Comm. Math. Phys. 92 (1983) p. 163. | Zbl | MR
:[G] Invariance Theory, The Heat Equation, and The Atiyah-Singer Index Theorem, Publish or Perish, (1984). | Zbl
:[K] Equivariant K-Theory and the Novikov Conjecture, Inventiones Math. 91, (1988) p. 147. | Zbl | MR
:[Ka] Homologie Cyclique et K-Théorie, Astérisque 149 (1987). | Zbl | MR | Numdam
:[L1] Superconnections and higher index theory, Geom. Funct. An. 2 (1992) p.421. | Zbl | MR
:[L2] Higher eta invariants, K-Theory 6 (1992) p. 191. | Zbl | MR
:[Lu] Novikov's Higher Signature and Families of Elliptic Operators, J.Diff. Geom 7, (1971), p. 229. | Zbl
:[Me] The Atiyah-Patodi-Singer Index Theorem, A. K Peters 1993. | Zbl | MR
:[Me2] Differential Analysis on Manifolds with Corners, in preparation.
:[MeNi] Homology of Pseudo-differential Operators I. Manifolds with Boundary, Preprint (1996).
- :[MP 1] Family of Dirac Operators, Boundaries and the b-Calculus, J. Diff. Geom. 46 (1997) p1. | Zbl
:[MP 2] An Index Theorem For Families of Dirac Operators on Odd-dimensional Manifolds with Boundary, J. Diff. Geom. To appear. | Zbl
:[MF] The Index of Elliptic Operators over C*-Algebras, Izv. Akad. Nauk SSSR, Ser. Mat. 43, (1979) p.831. | Zbl | MR
:[Pa] Inner Product Modules Over B*-Algebras, Trans AMS, 182, (1973). | Zbl | MR
:[P1] On The Index of Elliptic Operators on Manifolds with Boundary, Journ. Funct. Anal. 117, (1993), p.308. | Zbl | MR
:[Q] Superconnections and the Chern Character, Topology 24 (1985) p.89. | Zbl | MR
:[R] von Neumann Index Theorems for Manifolds With Boundary, J.Diff. Geom. (1992).
:[S] Some remarks on operator theory and index theory, Lect. Notes Math 575. | Zbl | MR
:[Sh 1] Spectral Theory of Elliptic pseudodifferential operators, Springer Verlag 1987.
:[Sh 2] L2-Riemann-Roch theorem for elliptic operators, GAFA (1995). | Zbl | MR
:[Wu] Higher noncommutative spectral flow, Preprint (1996).
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