Corks, Involutions, and Heegaard Floer Homology- Irving Dai (MIT)
Abstract: We introduce and study a set of Floer-theoretic invariants aimed at detecting corks. Our invariants obstruct the extension of a given involution over any homology ball, rather than a particular contractible manifold. As an application, we define a modification of the homology cobordism group which takes into account an involution on each homology sphere, and prove that this admits an infinitely-generated subgroup of strongly non-extendable corks. We establish several new families of corks and prove that various known examples are strongly non-extendable. This is joint work with Matthew Hedden and Abhishek Mallick. This talk will be complementary to the talk given by Abhishek Mallick (in the "Knots, Surfaces, and 4-Manifolds" topic group), and will discuss the Heegaard Floer theory underlying various detection results.
Knot Floer homology and relative adjunction inequalities- Katherine Raoux (Michigan State University)
Abstract: In this talk, we present a relative adjunction inequality for 4-manifolds with boundary. We begin by constructing generalized Heegaard Floer tau-invariants associated to a knot in a 3-manifold and a nontrivial Floer class. Given a 4-manifold with boundary, the tau-invariant associated to a Floer class provides a lower bound for the genus of a properly embedded surface, provided that the Floer class is in the image of the cobordism map induced by the 4-manifold. We will also discuss several applications to links and contact manifolds. This is joint work with Matt Hedden.
Involutive Heegaard Floer homology and surgeries- Ian Zemke (Princeton University)
Abstract: In this talk, we investigate the behavior of involutive Heegaard Floer homology with respect to surgeries. We prove several surgery exact sequences, and also a mapping cone formula, for involutive Heegaard Floer homology. In this talk, we will describe a few elements of the proof, and also some applications to the homology cobordism group. This project is joint work in progress with Kristen Hendricks, Jen Hom and Matt Stoffregen.