Ozsvath-Szabo’s bordered invariant and three strand pretzel knots.

Daniel Waite (University of Glasgow)

Friday 4th October 13:00-14:00 Maths 311B

Abstract

Recently, P. Ozsvath and Z. Szabo developed a divide and conquer algorithm to associate an algebraic invariant to an oriented knot diagram, conjecturally equivalent to a version of knot Floer homology. In this talk, I will give a (very) short introduction to classical knot Floer homology as motivation, before moving on to describe the algebraic objects used by Ozsvath and Szabo in the construction of their invariant. This algebraic invariant has generators in one-to-one correspondence with decorated knot projections called Kauffman states. Three strand pretzel knots are a family of knots with particularly well structured Kauffman states, and I will describe how one can use inductive methods to determine this algebraic invariant for three strand pretzel knots.

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