Anchored foams and annular homology

Akhmechet, Rostislav; Khovanov, Mikhail

doi:10.2140/agt.2023.23.3129

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Anchored foams and annular homology

Rostislav Akhmechet and Mikhail Khovanov

Algebraic & Geometric Topology 23 (2023) 3129–3204

DOI: 10.2140/agt.2023.23.3129

Abstract

We describe equivariant $SL (2)$ and $SL (3)$ homology for links in the thickened annulus via foam evaluation. The thickened annulus is replaced by $3$ –space with a distinguished line in it. Generators of state spaces for annular webs are represented by foams with boundary that may intersect the distinguished line; intersection points, called anchor points, contribute additional terms, reminiscent of square roots of the Hessian, to the foam evaluation. Both oriented and unoriented $SL (3)$ foams are treated.

Keywords

Khovanov homology, annular homology, foams, foam evaluation

Mathematical Subject Classification

Primary: 57K18

Secondary: 18N25, 57K16

References

Publication

Received: 9 June 2021

Revised: 5 April 2022

Accepted: 18 May 2022

Published: 26 September 2023

Authors

Rostislav Akhmechet
Department of Mathematics Columbia University New York, NY United States

Mikhail Khovanov
Department of Mathematics Johns Hopkins University Baltimore, MD United States

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Volume 23, issue 7 (2023)