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 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 کاملA Note on Vassiliev Invariants of Quasipositive Knots
It has been known that any Alexander polynomial of a knot can be realized by a quasipositive knot. In this paper we prove a generalization of that result: for any oriented knot K and any natural number n there exists a quasipositive knot Q whose Vassiliev invariants of order less than or equal to n coincide with those of K. A quasipositive braid is a product of conjugates of a positive standard...
متن کاملHigher-order Genera of Knots
For certain classes of knots we define geometric invariants called higher-order genera. Each of these invariants is a refinement of the slice genus of a knot. We find lower bounds for the higherorder genera in terms of certain von Neumann ρ-invariants, which we call higher-order signatures. The higher-order genera offer a refinement of the Grope filtration of the knot concordance group.
متن کاملGenera of Knots and Vassiliev Invariants
We prove that there is no non-constant Vassiliev invariant which is constant on alternating knots of infinitely many genera (contrasting the existence of the Conway Vassiliev invariants, which vanish on any finite set of genera) and that a (non-constant) knot invariant with values bounded by a funciton of the genus, in particular any invariant depending just on genus, signature and maximal degr...
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ژورنال
عنوان ژورنال: Topology and its Applications
سال: 1998
ISSN: 0166-8641
DOI: 10.1016/s0166-8641(97)00110-7