Homology of pseudo-differential operators on manifolds with fibered boundaries

Journal fur die Reine und Angewandte Mathematik

Volumn , Issue 547, 2002, Pages 207-234

  Lauter, Robert ^a   Moroianu, Sergiu ^b  

^a JOHANNES GUTENBERG UNIVERSITY   (Germany)

^b INSTITUTE OF MATHEMATICS   (Romania)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0036265015     PISSN: 00754102     EISSN: None     Source Type: Journal    
DOI: 10.1515/crll.2002.052     Document Type: Article

References (26)

1. M. Adler, On a trace functional for formal pseudo-differential operators and the symplectic structure of Korteweg-de Vries type equations, Invent. Math. 50 (1979), 219-248.
2. M. Benameur and V. Nistor, Homology of complete symbols and non-commutative geometry, preprint. June 2000.
3. J.-L. Brylinski, A differential complex for Poisson manifolds, J. Diff. Geom. 28 (1988), 93-114.
4. J.-L. Brylinski and E. Getzler, The homology of algebras of pseudodifferential operators and the non-commutative residue, K-theory 1 (1987), 385-403.
5. A. Connes, Noncommutative differential geometry, Inst. Hautes Ét. Sci. Publ. Math. 62 (1985), 257-360.
6. V. Guillemin, A new proof of Weyl's formula on the asymptotic distribution of eigenvalues, Adv. Math. 55 (1985), 131-160.
7. R. Lauter and S. Moroianu, On the index formula of Melrose and Nistor, Preprint Nr. 3, IMAR, Bucharest, March 2000.
8. R. Lauter and S. Moroianu, Fredholm theory for degenerate pseudodifferential operators on manifolds with fibred boundaries, Comm. Part. Diff. Equ. 26 (2001), 233-283.
9. J.-L Loday, Cyclic homology. Grundl. Math. Wiss. 301 Springer-Verlag, Berlin - Heidelberg - New York 1992.
10. Yu. I. Manin, Algebraic aspects of nonlinear differential equations, J. Sov. Math. 11 (1979), 1-122.
11. R. R. Mazzeo, Elliptic theory of differential edge operators I, Comm. Part. Diff. Equ. 16 (1991), 1615-1664.
12. J. McCleary, User's guide to spectral sequences, second edition, Publish or Perish, Inc., Wilmington 1985.
13. R. B. Melrose. Introduction to microlocal analysis, Lecture Notes - Spring 1990, Massachusetts Institute of Technology.
14. R. B. Melrose, Transformation of boundary value problems, Acta Math. 147 (1981), 149-236.
15. R. B. Melrose, The Atiyah-Patodi-Singer index theorem, volume 4 of Research Notes in Mathematics. A. K. Peters, Wellesley, Massachusetts, 1993.
16. R. B. Melrose, Spectral and scattering theory for the Laplacian on asymptotically Euclidean space, in: M. Ikawa, ed., Spectral and Scattering Theory, Lect. Notes Pure Appl. Math. 162 (1994), 85-130.
17. R. B. Melrose, Geometric scattering theory, Cambridge University Press, 1995.
18. R. B. Melrose, Fibrations, compactifications and algebras of pseudodifferential operators, in: L. Hörmander and A. Mellin, ed., Partial Differential Equations and Mathematical Physics (1996), 246-261.
19. R. B. Melrose, Geometric optics and the bottom of the spectrum, in: F. Colombini and N. Lerner, ed., Geometrical optics and related topics, Progr. nonlin. diff. equ. appl. 32, Birkhäuser, Basei - Boston - Berlin 1997.
20. R. B. Melrose and V. Nistor, Homology of pseudodifferential operators I. Manifolds with boundary, preprint, May 1996.
21. R. B. Melrose and V. Nistor, K-theory of C*-algebras of b-pseudodifferential operators, Geom. Funct. Anal. 8 (1998), 88-122.
22. S. Moroianu, Higher residues on the algebra of adiabatic pseudodifferential operators, PhD thesis, Massachusetts Institute of Technology, Cambridge. MA, May 1999.
23. R. Nest and E. Schrohe, Hochschild homology of Boutet de Monvel's algebra, in preparation.
24. M. Wodzicki, Noncommutative residue. I. Fundamentals, Springer Lect. Notes Math. 1289 (1987), 320-399.
25. M. Wodzicki, Cyclic homology of pseudodifferential operators and noncommutative Euler class, C. R. Acad. Sci. Paris Sér. 1 Math. 306(6) (1988), 321-325.
26. M. Wodzicki, The long exact sequence in cyclic homology associated with an extension of algebras, C. R. Acad. Sci. Paris Sér. I Math. 306(9) (1988), 399-403.