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

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1. [A1] M.F. Atiyah, K-theory, Benjamin, 1967. Zbl0159.53302MR36 #7130
2. [A2] M.F. Atiyah: Elliptic operators, discrete groups and von Neumann algebras, Astérisque, 32 (1976) p.43. Zbl0323.58015MR54 #8741
3. [ABP] Atiyah-Bott-Patodi: On The Heat Equation and The Index Theorem, Inv. Math. 19, (1968), p. 113. Zbl0257.58008
4. [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. Zbl0297.58008
5. [AS 1,3] M.F. Atiyah-I.Singer: The Index of Elliptic Operators I, III, Annals of Maths, 87 (1968) p. 484; p. 546. Zbl0164.24001MR38 #5245
6. [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. Zbl0551.46041
7. [BGV] N.Berline-E.Getzler-M.Vergne: Heat Kernels and Dirac Operators, Springer Verlag (1992). Zbl0744.58001
8. [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). Zbl0793.58032
9. [B] J-M.Bismut: The Atiyah-Singer Index Theorem for Families of dirac Operators: Two Heat Equations Proofs, Inv. Math. 83, (1986) p.91. Zbl0592.58047MR87g:58117
10. [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. Zbl0696.53021
11. [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). 
12. [Br] Breuer: Fredholm Theories in von Neumann algebras I, II, Math. Ann. 178 (1968), p 243; 180, (1969), p 313. Zbl0162.18701MR38 #2611
13. [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. Zbl0614.53034
14. [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. Zbl0493.53035MR84b:58109
15. [C] A.Connes: Noncommutative geometry, Academic Press, (1994). Zbl0818.46076MR95j:46063
16. [CM] A.Connes-H.Moscovici: Cyclic Cohomology, The Novikov Conjecture and Hyperbolic Groups, Topology, 29 No 3, (1990) p.345. Zbl0759.58047MR92a:58137
17. [DZ] X.Dai-W.Zhang: Higher spectral flow, Preprint (1996). 
18. [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). Zbl0698.35168
19. [Ge] E.Getzler: Pseudodifferential Operators on Supermanifolds and the Atiyah-Singer Index Theorem, Comm. Math. Phys. 92 (1983) p. 163. Zbl0543.58026MR86a:58104
20. [G] P.Gilkey: Invariance Theory, The Heat Equation, and The Atiyah-Singer Index Theorem, Publish or Perish, (1984). Zbl0565.58035
21. [K] G.Kasparov: Equivariant K-Theory and the Novikov Conjecture, Inventiones Math. 91, (1988) p. 147. Zbl0647.46053MR88j:58123
22. [Ka] M.Karoubi: Homologie Cyclique et K-Théorie, Astérisque 149 (1987). Zbl0648.18008MR89c:18019
23. [L1] J.Lott: Superconnections and higher index theory, Geom. Funct. An. 2 (1992) p.421. Zbl0777.58038MR93j:58128
24. [L2] J.Lott: Higher eta invariants, K-Theory 6 (1992) p. 191. Zbl0773.58026MR93j:58129
25. [Lu] G.Lustzig: Novikov's Higher Signature and Families of Elliptic Operators, J.Diff. Geom 7, (1971), p. 229. Zbl0265.57009
26. [Me] R.Melrose: The Atiyah-Patodi-Singer Index Theorem, A. K Peters 1993. Zbl0796.58050MR96g:58180
27. [Me2] R.Melrose: Differential Analysis on Manifolds with Corners, in preparation. 
28. [MeNi] R.Melrose-V.Nistor: Homology of Pseudo-differential Operators I. Manifolds with Boundary, Preprint (1996). 
29. [MP 1] R.Melrose-P.Piazza: Family of Dirac Operators, Boundaries and the b-Calculus, J. Diff. Geom. 46 (1997) p1. Zbl0955.58020
30. [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. Zbl0920.58053
31. [MF] A.Mishenko-A.Fomenko: The Index of Elliptic Operators over C*-Algebras, Izv. Akad. Nauk SSSR, Ser. Mat. 43, (1979) p.831. Zbl0416.46052MR81i:46075
32. [Pa] W.Paschke: Inner Product Modules Over B*-Algebras, Trans AMS, 182, (1973). Zbl0239.46062MR50 #8087
33. [P1] P.Piazza: On The Index of Elliptic Operators on Manifolds with Boundary, Journ. Funct. Anal. 117, (1993), p.308. Zbl0793.58035MR94h:58160
34. [Q] D.Quillen: Superconnections and the Chern Character, Topology 24 (1985) p.89. Zbl0569.58030MR86m:58010
35. [R] M.Ramachandran: von Neumann Index Theorems for Manifolds With Boundary, J.Diff. Geom. (1992). 
36. [S] I.Singer: Some remarks on operator theory and index theory, Lect. Notes Math 575. Zbl0444.47040MR57 #7699
37. [Sh 1] M.Shubin: Spectral Theory of Elliptic pseudodifferential operators, Springer Verlag 1987. 
38. [Sh 2] M.Shubin: L2-Riemann-Roch theorem for elliptic operators, GAFA (1995). Zbl0840.58045MR96f:58162
39. [Wu] F.Wu: Higher noncommutative spectral flow, Preprint (1996). 

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