34,263 research outputs found
State Cycles, Quasipositive Modification, and Constructing H-thick Knots in Khovanov Homology
We study Khovanov homology classes which have state cycle representatives,
and examine how they interact with Jacobsson homomorphisms and Lee's map
. 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.Comment: 42 pages, color figures. Version 2 revisions: an error was corrected
in Proposition 4.3, which requires a stronger hypothesis. This slightly
widens the classification theorem of section 4, and has led to small
revisions throughout. Theorem 4.7, which involved even all-1 state cycles,
has been removed, as it has grown into a forthcoming pape
Turaev genus, knot signature, and the knot homology concordance invariants
We give bounds on knot signature, the Ozsvath-Szabo tau invariant, and the
Rasmussen s invariant in terms of the Turaev genus of the knot.Comment: 15 pages, 5 figure
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