A quantitative Birman–Menasco finiteness theorem and its application to crossing number. Issue 4 (11th September 2022)

• Record Type: Journal Article
• Authors: Ito, Tetsuya
• Is Part Of: Journal of topology. Volume 15:Issue 4(2022)
• Page Start: 1794
• Page End: 1806
• Publication Date: 2022-09-11
• Subjects: Topology -- Periodicals; 514.05
• DOI: 10.1112/topo.12259
• Languages: English
• ISSNs: 1753-8416

Abstract

Abstract: Birman–Menasco proved that there are finitely many knots having a given genus and braid index. We give a quantitative version of the Birman–Menasco finiteness theorem, an estimate of the crossing number of knots in terms of genus and braid index. As applications, we give a solution of the braid index problem, the problem to determine the braid index of a given link, and provide estimates of the crossing number of connected sums or satellites.