منابع مشابه
Quasipositive Annuli (constructions of Quasipositive Knots and Links, Iv)
The modulus of quasipositivity q(K) of a knot K was introduced as a tool in the knot theory of complex plane curves, and can be applied to Legendrian knot theory in symplectic topology. It has also, however, a straightforward characterization in ordinary knot theory: q(K) is the supremum of the integers f such that the framed knot (K, f) embeds non-trivially on a fiber surface of a positive tor...
متن کاملPositive links are strongly quasipositive
Let S(D) be the surface produced by applying Seifert’s algorithm to the oriented link diagram D. I prove that if D has no negative crossings then S(D) is a quasipositive Seifert surface, that is, S(D) embeds incompressibly on a fiber surface plumbed from positive Hopf annuli. This result, combined with the truth of the “local Thom Conjecture”, has various interesting consequences; for instance,...
متن کاملA Characterization of Quasipositive Seifert Surfaces (constructions of Quasipositive Knots and Links, Iii) Lee Rudolph
Here, a surface is smooth, compact, oriented, and has no component with empty boundary. A Seifert surface is a surface embedded in S3. A subsurface S of a surface T is full if each simple closed curve on S that bounds a disk on T already bounds a disk on S. The definition of quasipositivity is recalled in §1, after a review of braided surfaces. The “only if” statement of the Characterization Th...
متن کاملLegendrian Graphs and Quasipositive Diagrams
In this paper we clarify the relationship between ribbon surfaces of Legendrian graphs and quasipositive diagrams by using certain fence diagrams. As an application, we give an alternative proof of a theorem concerning a relationship between quasipositive fiber surfaces and contact structures on S. We also answer a question of L. Rudolph concerning moves of quasipositive diagrams.
متن کاملMöbius Bands with a Quasipositive Fibred Hole
We prove that every knot in the 3-space bounds an embedded punctured Möbius band whose other boundary component is a quasipositive fibred knot.
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ژورنال
عنوان ژورنال: Topology and its Applications
سال: 2020
ISSN: 0166-8641
DOI: 10.1016/j.topol.2020.107495