An sl(2) tangle homology and seamed cobordisms
Geometric Topology
2007-09-10 v2
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.
Keywords
Cite
@article{arxiv.0707.3051,
title = {An sl(2) tangle homology and seamed cobordisms},
author = {Carmen Caprau},
journal= {arXiv preprint arXiv:0707.3051},
year = {2007}
}
Comments
77 pages, many figures; changes in referencing