On the genus defect of positive braid knots

Liechti, Livio

doi:10.2140/agt.2020.20.403

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the Journal

Editorial Board

Subscriptions

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN 1472-2739 (online)

ISSN 1472-2747 (print)

Author Index

To Appear

Other MSP Journals

On the genus defect of positive braid knots

Livio Liechti

Algebraic & Geometric Topology 20 (2020) 403–428

DOI: 10.2140/agt.2020.20.403

Abstract

We show that the difference between the Seifert genus and the topological $4$ –genus of a prime positive braid knot is bounded from below by an affine function of the minimal number of strands among positive braid representatives of the knot. We deduce that among prime positive braid knots, the property of having such a genus difference less than any fixed constant is characterised by finitely many forbidden surface minors.

Keywords

four-genus, genus defect, positive braid knot, surface minor, well-quasiorder

Mathematical Subject Classification 2010

Primary: 57M25, 57M27

Secondary: 06A06

References

Publication

Received: 5 November 2018

Revised: 22 March 2019

Accepted: 18 June 2019

Published: 23 February 2020

Authors

Livio Liechti
Department of Mathematics University of Fribourg Fribourg Switzerland

Volume 20, issue 1 (2020)