Vol. 295, No. 2, 2018

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ISSN: 0030-8730
Minimal braid representatives of quasipositive links

Kyle Hayden

Vol. 295 (2018), No. 2, 421–427
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
Authors
Kyle Hayden
Department of Mathematics
Boston College
Chestnut Hill, MA
United States