Groups, Geometry, and Topology Calendar

GGT Seminar: Bordered Perspectives on Exotic Phenomena in 4D

Event Type

Seminar/Symposium

Sponsor

Groups, Geometry, and Topology Seminar

Location

347 Altgeld Hall

Date

Dec 5, 2024   11:00 am - 12:00 pm  

Speaker

Gary Guth (Stanford)

Views

42

Abstract: In this talk, I will describe some joint works with Jesse Cohen and Sungkyung Kang. In short, these projects revolve around using tools from bordered Floer homology to detect exotic phenomena in dimension 4, by cutting up the objects of interest into simple pieces. First, I will describe a method for understanding certain symmetries of the Floer complex of certain knots in terms of symmetries of the Floer complexes of their complements. Kang and I refer to this as the ``LOT correspondence’’, and I will say a few words about using this correspondence to generate stably exotic corks. Second, I will describe work with Cohen which concerns interpreting certain cobordisms in terms of immersed curves. From this perspective, we explore how exotic surfaces can be constructed by studying satellites of slice disks.