A scanning algorithm for odd Khovanov homology

Schütz, Dirk

doi:10.2140/agt.2022.22.1287

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A scanning algorithm for odd Khovanov homology

Dirk Schütz

Algebraic & Geometric Topology 22 (2022) 1287–1324

DOI: 10.2140/agt.2022.22.1287

Abstract

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.

Keywords

Khovanov homology, concordance invariants, odd Khovanov homology

Mathematical Subject Classification

Primary: 57K18

Secondary: 57K10

References

Publication

Received: 21 August 2020

Revised: 1 March 2021

Accepted: 19 March 2021

Published: 25 August 2022

Authors

Dirk Schütz
Department of Mathematical Sciences Durham University Durham United Kingdom

Volume 22, issue 3 (2022)