The Michigan Mathematical Journal

Equivariant Khovanov Homology of Periodic Links

Wojciech Politarczyk

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The purpose of this paper is to construct and study equivariant Khovanov homology, a version of Khovanov homology theory for periodic links. Since our construction works regardless of the characteristic of the coefficient ring, it generalizes a previous construction by Chbili. We establish invariance under equivariant isotopies of links and study algebraic properties of integral and rational version of the homology theory. Moreover, we construct a skein spectral sequence converging to equivariant Khovanov homology and use this spectral sequence to compute, as an example, equivariant Khovanov homology of torus links T(n,2).

Article information

Michigan Math. J., Advance publication (2019), 31 pages.

Received: 11 December 2017
Revised: 31 July 2018
First available in Project Euclid: 8 August 2019

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Digital Object Identifier

Primary: 57M27: Invariants of knots and 3-manifolds
Secondary: 57M25: Knots and links in $S^3$ {For higher dimensions, see 57Q45} 57M60: Group actions in low dimensions 55N91: Equivariant homology and cohomology [See also 19L47] 18G40: Spectral sequences, hypercohomology [See also 55Txx]


Politarczyk, Wojciech. Equivariant Khovanov Homology of Periodic Links. Michigan Math. J., advance publication, 8 August 2019. doi:10.1307/mmj/1565251218.

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