Getting a handle on contact manifolds

Getting a handle on contact manifolds

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Kevin Sackel, MIT
Fine Hall 224

Analogous to Weinstein structures in symplectic geometry, there is a notion of convex structures in contact geometry. We discuss an explicit surgery theory for contact manifolds with convex structures, showing that they naturally decompose into handles, just like in the Weinstein setting. We also explore the relationship between these handle decompositions and Weinstein open books, proving as a corollary that every closed contact manifold has a convex structure, and hence a handle decomposition.