Showing distinctness of surface links by taking 2-dimensional braids

Inasa Nakamura

Vol. 278 (2015), No. 1, 235–251

DOI: 10.2140/pjm.2015.278.235

Abstract

For an oriented surface link $S$, we can take a satellite construction called a 2-dimensional braid over $S$, which is a surface link in the form of a covering over $S$. We demonstrate that 2-dimensional braids over surface links are useful for showing the distinctness of surface links. We investigate nontrivial examples of surface links with free abelian groups of rank two, concluding that their link types are infinitely many.

Keywords

surface link, 2-dimensional braid, chart, Roseman move, triple linking

Mathematical Subject Classification 2010

Primary: 57Q45

Secondary: 57Q35, 57M25

Milestones

Received: 7 October 2014

Revised: 27 March 2015

Accepted: 30 March 2015

Published: 30 September 2015