Minimal braid representatives of quasipositive links

Kyle Hayden

Vol. 295 (2018), No. 2, 421–427

DOI: 10.2140/pjm.2018.295.421

Abstract

We show that every quasipositive link has a quasipositive minimal braid representative, partially resolving a question posed by Orevkov. These quasipositive minimal braids are used to show that the maximal self-linking number of a quasipositive link is bounded below by the negative of the minimal braid index, with equality if and only if the link is an unlink. This implies that the only amphichiral quasipositive links are the unlinks, answering a question of Rudolph’s.

Keywords

quasipositive links, braid index, self-linking number, amphichirality

Mathematical Subject Classification 2010

Primary: 57M25

Secondary: 57R17

Milestones

Received: 21 April 2017

Accepted: 3 November 2017

Published: 11 April 2018