Date: Monday, January 28, 2013
Location: 3096 East Hall (3:00 PM to 4:00 PM)
Title: Computing the Khovanov Homology
Abstract: The focus of this talk will be the basic procedure for computing the Khovanov homology of a knot or link. We will begin by discussing the Jones polynomial, and how to compute it given the "n-cube of resolutions" for a picture of a link with n crossings. Khovanov homology is the so called "categorification" of the Jones Polynomial; the graded Euler characteristic of the Khovanov chain complex yields the Jones polynomial. This talk will be example driven; we will see that two knots sharing the same Jones polynomial can sometimes be differentiated by their Khovanov homology (so Khovanov homology is strictly stronger than the Jones polynomial) and that Khovanov homology can detect the unknot (it is unknown if the Jones polynomial can do this). One of the most appealing and interesting things about Khovanov homology, compared to other knot invariant homology theories, is its computability. We will explicitly compute the Khovanov homology for several knots using Dror Bar-Natan's Mathematica module.
Speaker: David Renardy
Institution: UM
Event Organizer: Tengren Zhang tengren@umich.edu
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