[Binghamton Geometry Topology Seminar] GT Seminar: Benjamin Thompson

[Jose Roman Aranda Cuevas]

Hi everyone,

This week we are pleased to have Benjamin Thompson (Cornell) speaking about
Khovanov homology, title and abstract below. This will be an *in-person
talk*, today Thursday at 2:50 pm in WH 100E.

We will also take the speaker to lunch at noon, and to dinner after the
talk. If you would like to join us for lunch, meet us today Thursday at 12
pm just outside WH100E. See you there!

Best,
Cary and Roman
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*Title*: Khovanov homology of rational tangles
*Abstract*: Links are fundamental objects of study in low-dimensional
topology, and are generalized by tangles. One of the most well-studied link
invariants, the Jones polynomial, was generalized by Khovanov to a homology
theory in the late 90s, before being extended to tangles in 2004 by
Bar-Natan. Working with tangles instead of links in Khovanov homology can
greatly simplify calculations and more easily shed light on the underlying
properties of the theory. In this talk we examine a subclass of tangles
known as rational tangles, and show that their Bar-Natan homology can be
computed with a string replacement algorithm. This essentially makes
computing Khovanov homology for rational knots trivial, and provides an
elementary explanation of the resulting homological phenomena.
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