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Homology of pseudodifferential operators on manifolds with fibered cusps

Authors: Robert Lauter and Sergiu Moroianu
Journal: Trans. Amer. Math. Soc. 355 (2003), 3009-3046
MSC (2000): Primary 58J42, 58J20
Published electronically: April 24, 2003
MathSciNet review: 1974673
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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.

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Additional Information

Robert Lauter
Affiliation: Fachbereich 17 - Mathematik, Universität Mainz, D-55099 Mainz, Germany

Sergiu Moroianu
Affiliation: Institutul de Matematică al Academiei Române, P.O. Box 1-764, RO-70700 Bucharest, Romania

Received by editor(s): July 15, 2002
Received by editor(s) in revised form: January 16, 2003
Published electronically: April 24, 2003
Additional Notes: Moroianu was partially supported by a DFG-grant (436-RUM 17/7/01) and by the European Commission RTN HPRN-CT-1999-00118 Geometric Analysis.
Article copyright: © Copyright 2003 American Mathematical Society