Speaker: Jacob Pichelmeyer

Title: Invariants of 4-manifolds via link homology

Place/Time: Friday, Oct 18, 2:30-3:20pm, Seaton 1063

Abstract: Gauge theory has long been the dominant source for invariants of smooth 4-manifolds. Famous for being both powerful and difficult, gauge theory has intimidated and baffled many topologists. Work by Khovanov in 2000 established an algebraic theory (the so-called Khovanov homology) which has since been used to recreate some results of gauge theory by means of combinatorial methods. The surge in popularity of Khovanov homology is due not only to it's power but also to it's accessibility. Recent work by Morrison, Walker, and Wedrich establishes the sweep-around property. This property allows the integration of 4-categories over oriented smooth 4-manifolds. Subsequently, to a given oriented smooth 4-manifold W with link L in it's boundary, a family of triply-graded abelian groups may be assigned. This family is a 4-manifold invariant computed independently of gauge theory. In this talk, we provide an outline for the paper by Morrison, Walker, and Wedrich along with some details of it's more important points.