Anchored foams and annular homology

Rostislav Akhmechet; Mikhail Khovanov

doi:10.2140/agt.2023.23.3129

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arXiv · 2105.00921

Anchored foams and annular homology

Rostislav Akhmechet·Mikhail Khovanov

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Abstract

We describe equivariant SL(2) and SL(3) homology for links in the solid torus via foam evaluation. The solid torus 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 in the paper.

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Rostislav Akhmechet, Mikhail Khovanov. 2021-05-03. Anchored foams and annular homology. https://doi.org/10.2140/agt.2023.23.3129

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