State Cycles, Quasipositive Modification, and Constructing H-thick Knots in Khovanov Homology

Andrew Elliott

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arXiv · 0901.4039

State Cycles, Quasipositive Modification, and Constructing H-thick Knots in Khovanov Homology

Andrew Elliott

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Abstract

We study Khovanov homology classes which have state cycle representatives, and examine how they interact with Jacobsson homomorphisms and Lee's map $Φ$. As an application, we describe a general procedure, quasipositive modification, for constructing H-thick knots in rational Khovanov homology. Moreover, we show that specific families of such knots cannot be detected by Khovanov's thickness criteria. We also exhibit a sequence of prime links related by quasipositive modification whose width is increasing.

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Andrew Elliott. 2009-06-09. State Cycles, Quasipositive Modification, and Constructing H-thick Knots in Khovanov Homology. https://arxiv.org/abs/0901.4039

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