#### Volume 13, issue 3 (2013)

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Odd Khovanov homology

### Peter S Ozsváth, Jacob Rasmussen and Zoltán Szabó

Algebraic & Geometric Topology 13 (2013) 1465–1488
##### 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
Primary: 57M25
Secondary: 57R58
##### 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