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Contact manifolds and automorphisms

Event Category:
Reading Seminar on Automorphism Groups of Manifolds
Kevin Sackel

In this talk, we are mostly interested in phenomena related to automorphism groups which are captured by contact geometry. To begin, we will discuss the basics of contact geometry, including basic definitions. This includes the tight vs overtwisted dichotomy, which is fundamental to the field. We will then focus on automorphisms in two manners. First, from an (exact) symplectic automorphism of certain symplectic manifolds (Liouville manifolds), one may cook up a contact manifold. This includes the case of Dehn twists along Lagrangian spheres which we have previously discussed. Second, we explain recent work of Eduardo Fernandez and Juan Munoz-Echaniz, who proved that for connected sums of certain contact 3-manifolds, performing a square Dehn twist in the connecting region (as constructed by Gompf in this setting) is an exotic contactomorphism.

Tuesday, October 17, 2023 - 4:00pm
LGRT 1685