University of Arkansas Topology Seminar: 9/19/2013

Speaker: Dan Rutherford

Title: Augmentations of the Legendrian contact homology algebra

Abstract: Legendrian contact homology is an invariant for Legendrian submanifolds of contact manifolds that enjoys functorial properties with respect to certain Lagrangian cobordisms. The invariant is given by a differential graded algebra (DGA) whose differential is defined via counting holomorphic disks in the symplectization of the given contact manifold. While the differential is difficult to compute in general, for Legendrian knots in ℝ3 the computation may be made in a combinatorial manner. One way to obtain information from the DGA is to consider augmentations which are homomorphisms from the DGA into a base field. The presence of an augmentation allows for finite dimensional linearized homology groups to be extracted from the infinite dimensional DGA. Time permitting, we will discuss some geometric constructions of augmentations from Lagrangian cobordisms and generating families and consequences for the corresponding linearized homology groups.