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Contact topology and geometry in high dimensions (Prof. Bahar Acu)
April 27 @ 4:15 pm - 5:30 pm
Title: Contact topology and geometry in high dimensions
Speaker: Bahar Acu, Department of Mathematics, Pitzer College
Abstract: A very useful strategy in studying topological manifolds is to factor them into “smaller” pieces. An open book decomposition of an n-manifold (the open book) is a special map (fibration) that helps us study our manifold in terms of its (n-1)-dimensional submanifolds (i.e. fibers=the pages) and (n-2)-dimensional boundary of these submanifolds (the binding). Open books provide a natural framework for studying topological properties of certain geometric structures on smooth manifolds such as “contact structures”. Thanks to open books, contact manifolds, odd dimensional manifolds carrying these geometric structures, can be studied from an entirely topological viewpoint. For example, every contact 3-manifold can be presented as an open book whose pages are surfaces and binding is a knot/link. In this talk, we will talk about higher-dimensional contact manifolds and provide a setting where we study these manifolds in terms of 3D open books. We present various results along with examples concerning geometric and topological aspects of these manifolds.