Twisting, Stabilization, and Knot Floer Homology

Soheil Azarpendar (University of Oxford)

Monday 3rd November 15:00-16:00
Maths 311B

Abstract

A twisting operation on a knot K involves performing a series of full twists on a set of parallel strands. The asymptotic behavior of knot invariants as the number of twists increases has been studied in various contexts — including the Alexander polynomial (Torres), the hyperbolic geometry of knot complements (Thurston), and Khovanov homology (Lee) — each revealing different stabilization phenomena. In this talk, I will present ongoing work investigating the asymptotic behavior of knot Floer homology under twisting. This work employs modern tools in the theory, such as bordered Floer homology and immersed curve invariants, to extend prior results.

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