State cycles, quasipositive modification, and constructing H-thick knots in Khovanov homology

[摘要] 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.

[发布机构] Rice University