Notes on link homology
Marta Asaeda, Mikhail Khovanov
TL;DR
This paper presents a series of lectures discussing the categorification of link invariants like the Jones and HOMFLY-PT polynomials through link homology groups, based on a summer school course.
Contribution
It provides an educational overview of the categorification process for link invariants and introduces link homology groups related to the Burau representation.
Findings
Categorification of the Burau representation
Construction of link homology groups for Jones polynomial
Extension to HOMFLY-PT polynomial
Abstract
This article consists of six lectures on the categorification of the Burau representation and on link homology groups which categorify the Jones and the HOMFLY-PT polynomial. The notes are based on the lecture course at the PCMI 2006 summer school in Park City, Utah.
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Taxonomy
TopicsTopological and Geometric Data Analysis · Geometric and Algebraic Topology