Swiss Knots 2011

Knot Theory and Algebra

Lake Thun, May 23-27

Does stable homotopy theory have anything to say about Khovanov homology?

Dr. Paul Turner's talk
Date: 26.05.11   Time: 17.30 - 18.20   Room: Gwatt Zentrum

Coauthors: B. Everitt and H.-W. Henn

Abstract: The underlying topological or geometrical properties measured by quantum invariants remain rather obscure. To better understand the situation it is natural to ask: given a quantum invariant defined on a certain type of object (for example knots), is it possible to associate to each object a space whose classical invariants yield the original quantum invariant? In this talk I will discuss some aspects of this question relevant to Khovanov homology. In particular I will describe how to produce an infinite loop space from a knot diagram whose homotopy groups are Khovanov homology. The homotopy type of this space is conjectured to be a knot invariant.