Algebra and geometry of link homology
Eugene Gorsky, Oscar Kivinen, Jos\'e Simental
TL;DR
This paper reviews the algebraic and geometric structures underlying link homology, focusing on Khovanov-Rozansky homology and its models via algebraic geometry, with recent advances and foundational properties.
Contribution
It provides a comprehensive overview of the algebraic and geometric models for link homology, including new insights and recent developments in the field.
Findings
Detailed description of Khovanov-Rozansky homology properties
Introduction of three algebro-geometric models for link homology
Summary of recent advances in the field
Abstract
These notes cover the lectures of the first named author at 2021 IHES Summer School on "Enumerative Geometry, Physics and Representation Theory" with additional details and references. They cover the definition of Khovanov-Rozansky triply graded homology, its basic properties and recent advances, as well as three algebro-geometric models for link homology: braid varieties, Hilbert schemes of singular curves and affine Springer fibers, and Hilbert schemes of points on the plane.
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Taxonomy
TopicsGeometric and Algebraic Topology · Homotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models