Algebraic & Geometric Topology

Odd Khovanov homology

Peter S Ozsváth, Jacob Rasmussen, and Zoltán Szabó

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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 . There is a reduced version which is a link invariant whose graded Euler characteristic is the normalized Jones polynomial.

Article information

Algebr. Geom. Topol., Volume 13, Number 3 (2013), 1465-1488.

Received: 9 September 2008
Revised: 11 July 2012
Accepted: 18 June 2012
First available in Project Euclid: 19 December 2017

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57M25: Knots and links in $S^3$ {For higher dimensions, see 57Q45}
Secondary: 57R58: Floer homology

Khovanov homology link knot


Ozsváth, Peter S; Rasmussen, Jacob; Szabó, Zoltán. Odd Khovanov homology. Algebr. Geom. Topol. 13 (2013), no. 3, 1465--1488. doi:10.2140/agt.2013.13.1465.

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