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Homology of pseudodifferential operators on manifolds with fibered cusps.

Homology of pseudodifferential operators on manifolds with fibered cusps.

Authors :
Robert Lauter
Sergiu Moroianu
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]

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