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

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

2009-01-26

arxiv.org/abs/0901.4039v2

Mathematics

Geometric Topology

42 pages, color figures. Version 2 revisions: an error was corrected in Proposition 4.3, which requires a stronger hypothesis.

Scientific paper

We study Khovanov homology classes which have state cycle representatives, and examine how they interact with Jacobsson homomorphisms and Lee's map $\Phi$. 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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