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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Homology of pseudodifferential operators on manifolds with fibered cusps
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by Robert Lauter and Sergiu Moroianu PDF
Trans. Amer. Math. Soc. 355 (2003), 3009-3046 Request permission

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
  • Email: lauter@mathematik.uni-mainz.de
  • Sergiu Moroianu
  • Affiliation: Institutul de Matematică al Academiei Române, P.O. Box 1-764, RO-70700 Bucharest, Romania
  • Email: moroianu@alum.mit.edu
  • 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.
  • © Copyright 2003 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 355 (2003), 3009-3046
  • MSC (2000): Primary 58J42, 58J20
  • DOI: https://doi.org/10.1090/S0002-9947-03-03294-X
  • MathSciNet review: 1974673