Volume 19, issue 1 (2015)
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Totally twisted Khovanov homology

Lawrence P Roberts
Geometry & Topology 19 (2015) 1–59
DOI: 10.2140/gt.2015.19.1
Abstract

We define a variation of Khovanov homology formally similar to totally twisted Heegaard–Floer homology. Over a certain field, this version of Khovanov homology has a completely explicit description in terms of the spanning trees of a link projection. We prove that this new theory is a link invariant and describe some of its properties. Finally, we provide the results of some computer computations of the invariant.

Keywords
Khovanov homology, spanning trees, knot homology
Mathematical Subject Classification 2010
Primary: 57M27
Secondary: 57M25
References
Publication
Received: 19 December 2011
Accepted: 17 April 2014
Published: 27 February 2015
Proposed: Peter S Ozsváth
Seconded: Yasha Eliashberg, Ciprian Manolescu
Authors
Lawrence P Roberts
Department of Mathematics
The University of Alabama
Box 820350
Tuscaloosa, AL 35487-0350
USA