## 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.## References

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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