Work

Signature and crossing number of links

Year: 2026

Type: article

Abstract: This paper investigates the relationship between the signature and the crossing number of knots and links. We refine existing theorems and provide a comprehensive classification of links with specific properties, particularly those with signatures that deviate by a fixed amount from their crossing numbers. The main results include the identification of all links for which the sum of the signature and crossing number equals 2, which are shown to be closures of positive 3-braids. Additionally, we explore the implications of these findings in the context of band surgeries and their applications to vortex knots and DNA topology.

Source: Journal of Knot Theory and Its Ramifications

DOI: 10.1142/s0218216526500240

Authors: Kai Ishihara, Kei Okada, Koya Shimokawa

Institutions: Hiroshima University, Saitama University, Tokyo University of Science, Ochanomizu University

Language: English

Topic: Geometric and Algebraic Topology

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Banff International Research Station for Mathematical Innovation and Discovery, Japan Society for the Promotion of Science

Awards: 結び目理論を用いた渦のトポロジーの研究, 結び目の配置と局所変形の研究