Algebraic & Geometric Topology

Odd Khovanov homology

Peter S Ozsváth, Jacob Rasmussen, and Zoltán Szabó

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

Article information

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

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

Permanent link to this document
https://projecteuclid.org/euclid.agt/1513715589

Digital Object Identifier
doi:10.2140/agt.2013.13.1465

Mathematical Reviews number (MathSciNet)
MR3071132

Zentralblatt MATH identifier
1297.57032

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

Keywords
Khovanov homology link knot

Citation

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. https://projecteuclid.org/euclid.agt/1513715589


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References

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