Residues and homology for pseudodifferential operators on foliations

M. T. Benameur, V. Nistor

Research output: Contribution to journalArticlepeer-review

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Abstract

We study the Hochschild homology groups of the algebra of complete symbols on a foliated manifold (M, F). The first step is to relate these groups to the Poisson homology of (M, F) and of other related foliated manifolds. We then establish several general properties of the Poisson homology groups of foliated manifolds. As an example, we completely determine these Hochschild homology groups for the algebra of complete symbols on the irrational slope foliation of a torus (under some diophantine approximation assumptions). We also use our calculations to determine all residue traces on algebras of pseudodifferential operators along the leaves of a foliation.

Original languageEnglish (US)
Pages (from-to)75-108
Number of pages34
JournalMathematica Scandinavica
Volume94
Issue number1
DOIs
StatePublished - 2004

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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