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On a triply graded Khovanov homology

Krzysztof K. Putyra

Krzysztof K. Putyra

ETHZ, Institute for Theoretical Studies, Clausiusstrasse 47, 8092 Zurich, Switzerland

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https://doi.org/10.1142/S0218216516400113Cited by:1 (Source: Crossref)

Abstract

Cobordisms are naturally bigraded and we show that this grading extends to Khovanov homology, making it a triply graded theory. Although the new grading does not make the homology a stronger invariant, it can be used to show that odd Khovanov homology is multiplicative with respect to disjoint unions and connected sums of links; same results hold for the generalized Khovanov homology defined by the author in his previous work. We also examine the module structure on both odd and even Khovanov homology, in particular computing the effect of sliding a basepoint through a crossing on the integral homology.

Keywords:

AMSC: 57M25, 57M27, 55N35, 18G60

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