Geometry with a Twist: The Restricted World of Legendrian Links
Prof. Lisa Traynor, Bryn Mawr College
Abstract: Contact manifolds are smooth manifolds that have an extra geometric structure — with roots in physics — given by a “twisting” hyperplane field. Legendrian submanifolds are the maximal dimensional integral submanifolds of the hyperplane field. For example, a contact structure on Euclidean 3-space is given by a field of 2-dimensional planes, and its Legendrian submanifolds are smooth knots and links that have restricted shapes and movements. A motivating question is to understand when two Legendrian submanifolds, which are equivalent as smooth submanifolds, are not equivalent as Legendrian submanifolds. Through a series of examples, I will introduce Legendrian submanifolds and Legendrian invariants of increasingly sophisticated depths.
Tea and refreshments available from 3:00-3:25 p.m. in the Assmus Conference Room (CU 212).
