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A sign assignment in totally twisted Khovanov homology

Andrew Manion
Algebraic & Geometric Topology 14 (2014) 753–767
DOI: 10.2140/agt.2014.14.753
Abstract

We lift the characteristic-2 totally twisted Khovanov homology of Roberts and Jaeger to a theory with ℤ coefficients. The result is a complex computing reduced odd Khovanov homology for knots. This complex is equivalent to a spanning-tree complex whose differential is explicit modulo a sign ambiguity coming from the need to choose a sign assignment in the definition of odd Khovanov homology.

Keywords
odd Khovanov homology
Mathematical Subject Classification 2010
Primary: 57M25
Secondary: 57M27
References
Publication
Received: 9 June 2012
Revised: 16 September 2013
Accepted: 19 September 2013
Published: 30 January 2014
Authors
Andrew Manion
Department of Mathematics
Princeton University
Princeton, NJ 08544
USA