Odd Khovanov homology

Ozsváth, Peter S; Rasmussen, Jacob; Szabó, Zoltán

doi:10.2140/agt.2013.13.1465

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Odd Khovanov homology

Peter S Ozsváth, Jacob Rasmussen and Zoltán Szabó

Algebraic & Geometric Topology 13 (2013) 1465–1488

DOI: 10.2140/agt.2013.13.1465

Abstract

We describe an invariant of links in $S^{3}$ which is closely related to Khovanov’s Jones polynomial homology. Our construction replaces the symmetric algebra appearing in Khovanov’s definition with an exterior algebra. The two invariants have the same reduction modulo $2$ , but differ over $ℚ$ . There is a reduced version which is a link invariant whose graded Euler characteristic is the normalized Jones polynomial.

Keywords

Khovanov, homology, link, knot

Mathematical Subject Classification 2010

Primary: 57M25

Secondary: 57R58

References

Publication

Received: 9 September 2008

Revised: 11 July 2012

Accepted: 18 June 2012

Published: 30 April 2013

Authors

Peter S Ozsváth
Department of Mathematics Massachusetts Institute of Technology Cambridge, MA 02139 USA

Jacob Rasmussen
Department of Pure Mathematics and Mathematical Statistics University of Cambridge Cambridge CB3 0WB UK

Zoltán Szabó
Department of Mathematics Princeton University Fine Hall, Washington Road Princeton, NJ 08544 USA

Volume 13, issue 3 (2013)