Residues and homology for pseudodifferential operators on foliations

Details Residues and homology for pseudodifferential operators on foliations Residues and homology for pseudodifferential operators on foliations

2002-04-16

arxiv.org/abs/math/0204205v1

Mathematics

K-Theory and Homology

26 pages

Scientific paper

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.

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