Knot Floer homology and the unknotting number

IF 2 1区数学

Geometry & Topology Pub Date : 2018-10-11 DOI:10.2140/gt.2020.24.2435

Akram Alishahi, Eaman Eftekhary

引用次数: 19

Abstract

Given a knot K in S^3, let u^-(K) (respectively, u^+(K)) denote the minimum number of negative (respectively, positive) crossing changes among all unknotting sequences for K. We use knot Floer homology to construct the invariants l^-(K), l^+(K) and l(K), which give lower bounds on u^-(K), u^+(K) and the unknotting number u(K), respectively. The invariant l(K) only vanishes for the unknot, and is greater than or equal to the \nu^-(K). Moreover, the difference l(K)-\nu^-(K) can be arbitrarily large. We also present several applications towards bounding the unknotting number, the alteration number and the Gordian distance.

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结花同源性和解结数

给定S^3中的一个结点K，令u^-(K)(分别为u^+(K))表示K的所有解结序列中负(分别为正)交叉变化的最小个数。我们利用结花同调构造了l^-(K)、l^+(K)和l(K)不变量，分别给出了u^-(K)、u^+(K)和解结数u(K)的下界。不变量l(K)只在解结时消失，并且大于等于\nu^-(K)而且，l(K)- nu^-(K)的差值可以任意大。在解结数、改变数和戈氏距离的限定方面也给出了几种应用。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Geometry & Topology 数学-数学

自引率

5.00%

发文量

期刊介绍： Geometry and Topology is a fully refereed journal covering all of geometry and topology, broadly understood. G&T is published in electronic and print formats by Mathematical Sciences Publishers. The purpose of Geometry & Topology is the advancement of mathematics. Editors evaluate submitted papers strictly on the basis of scientific merit, without regard to authors" nationality, country of residence, institutional affiliation, sex, ethnic origin, or political views.