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Anchored foams and annular homology

Rostislav Akhmechet and Mikhail Khovanov

Algebraic & Geometric Topology 23 (2023) 3129–3204
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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