Stabilization in the braid groups I: MTWS
| dc.creator | Birman, Joan S | |
| dc.creator | Menasco, William W | |
| dc.date | 2003-10-18 | |
| dc.date | 2009-02-26 | |
| dc.date.accessioned | 2026-07-07T12:48:15Z | |
| dc.date.available | 2026-07-07T12:48:15Z | |
| dc.description | Choose any oriented link type X and closed braid representatives X[+], X[-] of X, where X[-] has minimal braid index among all closed braid representatives of X. The main result of this paper is a `Markov theorem without stabilization'. It asserts that there is a complexity function and a finite set of `templates' such that (possibly after initial complexity-reducing modifications in the choice of X[+] and X[-]which replace them with closed braids X[+]', X[-]') there is a sequence of closed braid representatives X[+]' = X^1->X^2->...->X^r = X[-]' such that each passage X^i->X^i+1 is strictly complexity reducing and non-increasing on braid index. The templates which define the passages X^i->X^i+1 include 3 familiar ones, the destabilization, exchange move and flype templates, and in addition, for each braid index m>= 4 a finite set T(m) of new ones. The number of templates in T(m) is a non-decreasing function of m. We give examples of members of T(m), m>= 4, but not a complete listing. There are applications to contact geometry, which will be given in a separate paper. | |
| dc.description | This is the version published by Geometry & Topology on 27 April 2006; part II (arXiv:math/0310280) is also published in GT volume 10 | |
| dc.identifier | https://arxiv.org/abs/math/0310279 | |
| dc.identifier | http://arxiv.org/abs/math/0310279 | |
| dc.identifier | Geom. Topol. 10 (2006) 413-540 | |
| dc.identifier | doi:10.2140/gt.2006.10.413 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/221990 | |
| dc.subject | Geometric Topology | |
| dc.subject | Group Theory | |
| dc.subject | 57M25, 57M50 | |
| dc.title | Stabilization in the braid groups I: MTWS | |
| dc.type | text |