Austin Christian, Cal Poly, San Luis Obispo

Title: Bypass moves in convex hypersurface theory

Abstract: In dimension 3, the convex surface theory developed by Giroux has proven to be an indispensable tool for contact topologists. The theory of convex hypersurfaces in higher dimensional contact manifolds has been established in recent years by Honda-Huang, who provided, among other things, a unique model for the generic degeneration of convexity in a 1-parameter family of hypersurfaces. Despite this abstract understanding of the model — known as a bypass — relatively few explicit computations with bypasses have appeared in the literature. In this talk, we present some basic ’moves’ which can be accomplished with bypass attachments and use them to produce exotic decompositions of convex surfaces in high dimensions. This work is joint with J. Breen.