Knot Floer homology and the gl(1|1) link invariant

Geometry/topology Seminar

Ina Petkova (Dartmouth College, Mathematics)

Monday, November 19, 2018 -
3:15pm to 4:15pm
Location: 
119 Physics

The Reshetikhin-Turaev construction for the standard representation of the quantum group gl(1|1) sends tangles to C(q)-linear maps in such a way that a knot is sent to its Alexander polynomial. After a brief review of this construction, I will give an introduction to tangle Floer homology — a combinatorial generalization of knot Floer homology which sends tangles to (homotopy equivalence classes of) bigraded dg bimodules. Finally, I will discuss how to see tangle Floer homology as a categorification of the Reshetikhin-Turaev invariant. This is joint work with Alexander Ellis and Vera Vertesi.

Last updated: 2018/12/16 - 10:21pm