Homological thickness of torus knots
نویسنده
چکیده
In this paper we show that the torus knots Tp,q for 3 ≤ p ≤ q are homologically thick. Even more, we show that we can reduce the number of twists q without changing certain part of homology, and consequently we show that there exists stable homology for torus knots conjectured in [4]. Also, we calculate Khovanov homology groups of low homological degree for torus knots, and we conjecture that the homological width of the torus knot Tp,q is at least p.
منابع مشابه
Homological thickness and stability of torus knots
In this paper we show that the non-alternating torus knots are homologically thick, i.e. that their Khovanov homology occupies at least three diagonals. Furthermore, we show that we can reduce the number of full twists of the torus knot without changing certain part of its homology, and consequently, we show that there exists stable homology of torus knots conjectured by Dunfield, Gukov and Ras...
متن کاملHomology of torus links
In this paper we show that there is a cut-off in the Khovanov homology of (2k, 2kn)-torus links, namely that the maximal homological degree of non-zero homology group of (2k, 2kn)-torus link is 2kn. Furthermore, we calculate explicitely the homology groups in homological degree 2kn and prove that it coincides with the centre of the ring H of crossingless matchings, introduced by M. Khovanov in ...
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 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 کاملRasmussen invariant and Milnor conjecture
These notes were written for a serie of lectures on the Rasmussen invariant and the Milnor conjecture, given at Winter Braids IV in February 2014. Introduction A torus knot is a knot in R3 which can be drawn without crossing on the surface of a trivially embedded solid torus. Up to mirror image, non trivial torus knots are classified by pairs {p, q} of coprime non negative integers. By conventi...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2005