Topology Seminar

About this event

Speaker: Autumn Thomas (University of Arkansas)

Title: Floer homology of satellite knots via immersed curves

Abstract : Take a knot P in the solid torus D² ⨉ S¹. Then, tie this solid torus into another knot K in S³. The resulting image, P(K), of the original knot P, is called a satellite knot. By Thurston Geometrization, every knot is either hyperbolic, a torus knot, or a satellite, so this is a reasonable class to draw attention to. In this talk, I will describe a recent diagrammatic technique of Chen for finding otherwise abstruse Heegaard Floer invariants of certain satellite knots. Along the way, I will introduce the evolution of bordered Floer homology from Heegaard Floer homology, why it lends itself to studying satellite and surgery operations, and how the recent immersed curve perspective by Hanselman, Rasmussen and Watson of these bordered invariants offers an elegant alternative. No experience with Floer homology is assumed.