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Homology and residues of adiabatic pseudodifferential operators

Published online by Cambridge University Press:  22 January 2016

Sergiu Moroianu
Sergiu Moroianu*
Affiliation:
Institutul de Matematică al Academiei Române, P. O. Box 1-764, RO-70700, Bucharest, Romania, [email protected]
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Abstract

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We compute the Hochschild homology groups of the adiabatic algebra Ψa(X), a deformation of the algebra of pseudodifferential operators Ψ(X) when X is the total space of a fibration of closed manifolds. We deduce the existence and uniqueness of traces on Ψa(X) and some of its ideals and quotients, in the spirit of the noncommutative residue of Wodzicki and Guillemin. We introduce certain higher homological versions of the residue trace. When the base of the fibration is S1, these functionals are related to the η function of Atiyah-Patodi-Singer.

Keywords

58J4258J20
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 175 , 2004 , pp. 171 - 221
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2004

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