Notions of positivity and the Ozsvath-Szabo concordance invariant

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dc.creatorHedden, Matthew
dc.date2005-09-21
dc.date.accessioned2026-07-07T06:18:34Z
dc.date.available2026-07-07T06:18:34Z
dc.descriptionIn this paper we examine the relationship between various types of positivity for knots and the concodance invariant tau discovered by Ozsvath and Szabo and independently by Rasmussen. The main result shows that, for fibered knots, tau characterizes strong quasipositivity. This is quantified by the statement that for K fibered, tau(K)=g(K) if and only if K is strongly quasipositive. In addition, we survey existing results regarding tau and forms of positivity and highlight several consequences concerning the types of knots which are (strongly) (quasi) positive. For instance, we show that any knot known to admit a lens space surgery is strongly quasipositive and exhibit infinite families of knots which are not quasipositive.
dc.description13 pages, 3 figures
dc.identifierhttps://arxiv.org/abs/math/0509499
dc.identifierhttp://arxiv.org/abs/math/0509499
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/94777
dc.subjectGeometric Topology
dc.subjectSymplectic Geometry
dc.titleNotions of positivity and the Ozsvath-Szabo concordance invariant
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