Foliation C*-algebras on multiply fibred manifolds

Details Foliation C*-algebras on multiply fibred manifolds Foliation C*-algebras on multiply fibred manifolds

2010-12-09

arxiv.org/abs/1012.2023v2

Mathematics

Functional Analysis

10 pages. Results now apply to locally homogeneous families of foliations without assuming the Hormander condition

Scientific paper

Motivated by index theory for semisimple groups, we study the relationship between the foliation C^*-algebras on manifolds admitting multiple fibrations. Let F_1,...,F_r be a collection of smooth foliations of a manifold X. We impose a condition of local homegeneity on these foliations which ensures that they generate a foliation F under Lie bracket of tangential vector fields. We then show that the product of longitudinal smoothing operators along each F_j belongs to the C*-closure of the smoothing operators along F. An application to noncommutative harmonic analysis on compact Lie groups is presented.

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