Operator Algebra of Transversely Affine Foliations

Details Operator Algebra of Transversely Affine Foliations Operator Algebra of Transversely Affine Foliations

2007-11-06

arxiv.org/abs/0711.0790v2

Mathematics

Operator Algebras

9 pages, first part reorganized, typos corrected

Scientific paper

We establish a geometric condition that determines when a type III von
Neumann algebra arises from a foliation whose holonomy becomes affine with
respect to a suitable transverse coordinate system. Under such an assumption
the Godbillon-Vey class of the foliation becomes trivial in contrast to the
case considered in Connes's famous theorem.

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