Homology of pseudodifferential operators on manifolds with fibered cusps

Lauter, Robert; Moroianu, Sergiu

doi:10.1090/S0002-9947-03-03294-X

Homology of pseudodifferential operators on manifolds with fibered cusps
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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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