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Slideshow

Graduate Student Topology Seminar: Melissa Zhang

Date and time:
Boyd Room 628

 

Title: An Introduction to Khovanov homology

Abstract: I will give a hands-on introduction to Khovanov homology based on the first portion of Bar-Natan's excellent introduction (https://arxiv.org/abs/math/0201043). Just as singular homology associates a collection of groups (one for each dimension) to a topological space, Khovanov homology associates a collection of groups to a link. It can be computed from a link diagram via a very concrete algorithm; in this sense, it is often described as a "combinatorial" link invariant. In 2000, Khovanov introduced this invariant by "categorifying" an older link invariant -- the Jones polynomial. We will discuss how to obtain the Jones polynomial of a link from its Khovanov homology. From here, one can learn about the structure of Khovanov homology (e.g. long exact sequences, torsion), its relationship with other categorified invariants (e.g. Heegaard Floer homology), and much, much more. In the interest of time, I will only discuss the most significant application of Khovanov homology: Rasmussen's link concordance invariant s.

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