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2004 Homology and residues of adiabatic pseudodifferential operators
Sergiu Moroianu
Nagoya Math. J. 175: 171-221 (2004).

Abstract

We compute the Hochschild homology groups of the adiabatic algebra $\Psi_\alpha(X)$, a deformation of the algebra of pseudodifferential operators $\Psi(X)$ when $X$ is the total space of a fibration of closed manifolds. We deduce the existence and uniqueness of traces on $\Psi_\alpha(X)$ 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 $S^1$, these functionals are related to the $\eta$ function of Atiyah-Patodi-Singer.

Citation

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Sergiu Moroianu. "Homology and residues of adiabatic pseudodifferential operators." Nagoya Math. J. 175 171 - 221, 2004.

Information

Published: 2004
First available in Project Euclid: 27 April 2005

zbMATH: 1113.58012
MathSciNet: MR2085316

Subjects:
Primary: 58J42
Secondary: 47G30, 47L80, 58J28

Rights: Copyright © 2004 Editorial Board, Nagoya Mathematical Journal

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