Anchored foams and annular homology

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.

arXiv comment56 pages, many figures

References in corpus (17)

• Khovanov's homology for tangles and cobordisms
• Spiders for rank 2 Lie algebras
• Categorification of the Kauffman bracket skein module of I-bundles over surfaces
• sl(3) link homology
• The universal sl3-link homology
• On Khovanov's cobordism theory for su(3) knot homology
• Deformations of colored sl(N) link homologies via foams
• The sl_3 web algebra
• On knot Floer homology in double branched covers
• Annular Khovanov homology and knotted Schur-Weyl representations
• sl(3)-Foams and the Khovanov-Lauda categorification of quantum sl(k)
• Annular Evaluation and Link Homology
• Exact triangles for SO(3) instanton homology of webs
• Fixing the functoriality of Khovanov homology: a simple approach
• Functoriality for the su(3) Khovanov homology
• A deformation of instanton homology for webs
• Computer Bounds for Kronheimer-Mrowka Foam Evaluation