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Operator Algebra and Noncommutative Geometry Seminar Series
November 9, 2017 @ 3:30 pm - 4:30 pm
Lachlan MacDonald (UOW)
Foliations, operator algebras and the Godbillon-Vey invariant
Foliations formalise the intuitive notion of a “layered space”, in which we regard a manifold as being composed of lower-dimensional slices called leaves. While locally the slice structure of a foliation is very simple, globally the leaves of a foliation tend to twist and coalesce about each other in very complicated ways. This twisting is encoded in the “holonomy” of the foliation, which I will describe in the talk. I will also outline how operator algebras are built from the holonomy data of a foliation and how they may be used to study the topological and measure-theoretic properties of the foliation. The talk will be concluded with a discussion of the Godbillon-Vey invariant of foliations, which provides a measure of how much a foliation is tending to expand or contract as one travels along leaves.