New family of hyperbolic knots whose Upsilon invariants are convex

IF 0.5 4区数学 Q3 MATHEMATICS

Topology and its Applications Pub Date : 2025-05-27 DOI:10.1016/j.topol.2025.109441

Keisuke Himeno

引用次数: 0

Abstract

The Upsilon invariant of a knot is a concordance invariant derived from knot Floer homology theory. It is a piecewise linear continuous function defined on the interval

[0, 2]

. Borodzik and Hedden gave a question asking for which knots the Upsilon invariant is a convex function. It is known that the Upsilon invariant of any L-space knot, and a Floer thin knot after taking its mirror image, if necessary, as well, is convex. Also, we can make infinitely many knots whose Upsilon invariants are convex by the connected sum operation. In this paper, we construct hyperbolic knots with convex Upsilon invariants which are none of the above. To calculate the full knot Floer complex, we make use of a combinatorial method for

(1, 1)

-knots.

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Upsilon不变量为凸的新双曲结族

结的Upsilon不变量是由结花同调理论导出的一个和谐不变量。它是一个分段线性连续函数，定义在区间[0,2]上。Borodzik和Hedden提出了一个问题，对于哪些结点Upsilon不变量是凸函数。已知任何l空间结的Upsilon不变量是凸的，如有必要，取其镜像后的flower薄结也是凸的。此外，我们可以利用连通和运算得到无限多个Upsilon不变量为凸的结点。在本文中，我们构造了具有凸Upsilon不变量的双曲结点。为了计算完整的结花复合体，我们使用(1,1)-节的组合方法。

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

Topology and its Applications 数学-数学

CiteScore

1.20

自引率

33.30%

发文量

251

审稿时长

6 months

期刊介绍： Topology and its Applications is primarily concerned with publishing original research papers of moderate length. However, a limited number of carefully selected survey or expository papers are also included. The mathematical focus of the journal is that suggested by the title: Research in Topology. It is felt that it is inadvisable to attempt a definitive description of topology as understood for this journal. Certainly the subject includes the algebraic, general, geometric, and set-theoretic facets of topology as well as areas of interactions between topology and other mathematical disciplines, e.g. topological algebra, topological dynamics, functional analysis, category theory. Since the roles of various aspects of topology continue to change, the non-specific delineation of topics serves to reflect the current state of research in topology. At regular intervals, the journal publishes a section entitled Open Problems in Topology, edited by J. van Mill and G.M. Reed. This is a status report on the 1100 problems listed in the book of the same name published by North-Holland in 1990, edited by van Mill and Reed.