Topology Atlas | Conferences

Knots in the Triangle (Knots kNot in Washington)
April 29 - May 1, 2016
North Carolina State University
Raleigh NC, USA

Organizers
Valentina Harizanov (GWU), Jozef H. Przytycki (GWU), Yongwu Rong (GWU), Radmila Sazdanovic (NCSU), Alexander Shumakovitch (GWU), Hao Wu (GWU)

Conference Homepage


Elements of Khovanov Homology and Khovanov Homotopy
by
Louis H. Kauffman
Math, UIC, 851 South Morgan Street, Chicago, IL 6070-7045

This is both a research talk and an introductory talk about Khovanov homology.

We start with the bracket polynomial model of the Jones polynomial and discuss how

Khovanov homology is built from the states of the bracket polynomial by regarding

them as generating a small category. We discuss Bar-Natan’s tangle-cobordism

picture of Khovanov homology, and show how his 4Tu-Relation is obtained naturally

in the attempt to make the theory invariant under chain homotopy.

We show how the associated Frobenius algebras arise naturally and how all of this fits

together. We then examine the question of chain homotopy versus homotopy

and show how a judicious use of simplicial theory (the Dold-Kan Theorem)

produces natural spaces that behave well stably to give

a homotopy theory for Khovanov homology.

Date received: April 19, 2016

Copyright © 2016 by the author(s). The author(s) of this work and the organizers of the conference have granted their consent to include this abstract in Topology Atlas. Document # cbmk-39.