TL;DR
This paper provides an expository overview of Khovanov homology, covering its theoretical foundations, related invariants, and various applications in topology and algebra, aimed at graduate students.
Contribution
It offers a comprehensive, accessible introduction to Khovanov homology and its related concepts, integrating topological and algebraic perspectives.
Findings
Clarifies the relationship between the Jones polynomial and Khovanov homology
Explores applications of Khovanov homology in topology
Discusses spectral sequences and stable homotopy types related to Khovanov homology
Abstract
These are expository lecture notes from a graduate topics course taught by the author on Khovanov homology and related invariants. Major topics include the Jones polynomial, Khovanov homology, Bar-Natan's cobordism category, applications of Khovanov homology, some spectral sequences, Khovanov stable homotopy type, and skein lasagna modules. Topological and algebraic exposition are sprinkled throughout as needed.
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Taxonomy
TopicsGeometric and Algebraic Topology · Homotopy and Cohomology in Algebraic Topology · Computability, Logic, AI Algorithms