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Homology of pseudodifferential operators on manifolds with fibered cusps.
Homology of pseudodifferential operators on manifolds with fibered cusps.
- Source :
-
Transactions of the American Mathematical Society . Aug2003, Vol. 355 Issue 8, p3009-3046. 38p. - Publication Year :
- 2003
-
Abstract
- The Hochschild homology of the algebra of pseudodifferential operators on a manifold with fibered cusps, introduced by Mazzeo and Melrose, is studied and computed using the approach of Brylinski and Getzler. One of the main technical tools is a new convergence criterion for tri-filtered half-plane spectral sequences. Using trace-like functionals that generate the $0$-dimensional Hochschild cohomology groups, the index of a fully elliptic fibered cusp operator is expressed as the sum of a local contribution of Atiyah-Singer type and a global term on the boundary. We announce a result relating this boundary term to the adiabatic limit of the eta invariant in a particular case. [ABSTRACT FROM AUTHOR]
- Subjects :
- *PSEUDODIFFERENTIAL operators
*HOMOLOGY theory
Subjects
Details
- Language :
- English
- ISSN :
- 00029947
- Volume :
- 355
- Issue :
- 8
- Database :
- Academic Search Index
- Journal :
- Transactions of the American Mathematical Society
- Publication Type :
- Academic Journal
- Accession number :
- 10103779
- Full Text :
- https://doi.org/10.1090/S0002-9947-03-03294-X