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Notes on Khovanov homology

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arxiv 2501.03115 v1 pith:LA7DBKMH submitted 2025-01-06 math.GT math.QA

Melissa Zhang This is my paper · ORCID
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keywords khovanovhomologynotestopicsalgebraicapplicationsauthorbar-natan
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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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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Lecture notes on link homologies and knotted surfaces

    math.GT 2025-07 conditional novelty 2.0 of 10

    Lecture notes presenting the cobordism maps on Khovanov and link Floer homology as invariants of knotted surfaces, with worked examples and exercises.

  2. Lectures on SL(3) foams and link homology

    math.QA 2025-07 conditional novelty 1.0 of 10

    This is an expository review of SL(3) foam evaluation and its use in categorifying the Kuperberg quantum invariant, with no new theorems.

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