Volume 22, issue 3 (2022)

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A scanning algorithm for odd Khovanov homology

Dirk Schütz

Algebraic & Geometric Topology 22 (2022) 1287–1324

We adapt Bar-Natan’s scanning algorithm for fast computations in (even) Khovanov homology to odd Khovanov homology. We use a mapping cone construction instead of a tensor product, which allows us to deal efficiently with the more complicated sign assignments in the odd theory. The algorithm has been implemented in a computer program. We also use the algorithm to determine the odd Khovanov homology of 3–strand torus links.

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Khovanov homology, concordance invariants, odd Khovanov homology
Mathematical Subject Classification
Primary: 57K18
Secondary: 57K10
Received: 21 August 2020
Revised: 1 March 2021
Accepted: 19 March 2021
Published: 25 August 2022
Dirk Schütz
Department of Mathematical Sciences
Durham University
United Kingdom