Nonslice linear combinations of iterated torus knots
نویسندگان
چکیده
In 1976, Rudolph asked whether algebraic knots are linearly independent in the knot concordance group. This paper uses twisted Blanchfield pairings to answer this question affirmative for new large families of knots.
منابع مشابه
On iterated torus knots and transversal knots
A knot type is exchange reducible if an arbitrary closed n{braid representative K of K can be changed to a closed braid of minimum braid index nmin(K) by a nite sequence of braid isotopies, exchange moves and {destabilizations. (See Figure 1). In the manuscript [6] a transversal knot in the standard contact structure for S3 is de ned to be transversally simple if it is characterized up to trans...
متن کاملA Ρ–invariant of Iterated Torus Knots
We compute ρ–invariant for iterated torus knots K for the standard representation π1(S \ K) → Z given by abelianisation. For algebraic knots, this invariant turns out to be very closely related to an invariant of a plane curve singularity, coming from algebraic geometry.
متن کاملAn addendum on iterated torus knots
In Theorem 1.2 of the paper [M1] the author claimed to have proved that all transversal knots whose topological knot type is that of an iterated torus knot (we call them cable knots) are transversally simple. That theorem is false, and the Erratum [M2] identifies the gap. The purpose of this paper is to explore the situation more deeply, in order to pinpoint exactly which cable knots are not tr...
متن کاملStudying Uniform Thickness Ii: Transversally Non-simple Iterated Torus Knots
We prove that an iterated torus knot type fails the uniform thickness property (UTP) if and only if all of its iterations are positive cablings, which is precisely when an iterated torus knot type supports the standard contact structure. We also show that all iterated torus knots that fail the UTP support cabling knot types that are transversally non-simple.
متن کاملStudying Uniform Thickness I: Legendrian Simple Iterated Torus Knots
We prove that the class of topological knot types that are both Legendrian simple and satisfy the uniform thickness property (UTP) is closed under cabling. An immediate application is that all iterated cabling knot types that begin with negative torus knots are Legendrian simple. We also examine, for arbitrary numbers of iterations, iterated cablings that begin with positive torus knots, and es...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Algebraic & Geometric Topology
سال: 2023
ISSN: ['1472-2739', '1472-2747']
DOI: https://doi.org/10.2140/agt.2023.23.765