An sl(2) tangle homology and seamed cobordisms

Abstract

We construct a bigraded (co)homology theory which depends on a parameter a, and whose graded Euler characteristic is the quantum sl(2) link invariant. We follow Bar-Natan's approach to tangles on one side, and Khovanov's sl(3) theory for foams on the other side. Our theory is properly functorial under tangle cobordisms, and a version of the Khovanov sl(2) invariant (or Lee's modification of it) corresponds to a=0 (or a=1). In particular, our construction naturally resolves the sign ambiguity in the functoriality of Khovanov's sl(2) homology theory.

arXiv comment77 pages, many figures; changes in referencing

References in corpus (2)

• Khovanov's homology for tangles and cobordisms
• An invariant of link cobordisms from Khovanov homology

Cited by in corpus (8)

• Khovanov homology is a skew Howe 2-representation of categorified quantum sl(m)
• An introduction to diagrammatic algebra and categorified quantum sl(2)
• An odd categorification of quantum sl(2)
• The universal sl(2) cohomology via webs and foams
• Fixing the functoriality of Khovanov homology: a simple approach
• On the sl(2) foam cohomology computations
• Frobenius algebras and skein modules of surfaces in 3-manifolds
• A categorification of the quantum sl(N)-link polynomials using foams