A family of pseudo-Anosov braids with small dilatation
| dc.creator | Hironaka, Eriko | |
| dc.creator | Kin, Eiko | |
| dc.date | 2009-04-03 | |
| dc.date.accessioned | 2026-07-07T13:00:19Z | |
| dc.date.available | 2026-07-07T13:00:19Z | |
| dc.description | This paper describes a family of pseudo-Anosov braids with small dilatation. The smallest dilatations occurring for braids with 3, 4 and 5 strands appear in this family. A pseudo-Anosov braid with 2g+1 strands determines a hyperelliptic mapping class with the same dilatation on a genus-g surface. Penner showed that logarithms of least dilatations of pseudo-Anosov maps on a genus-g surface grow asymptotically with the genus like 1/g, and gave explicit examples of mapping classes with dilatations bounded above by log 11/g. Bauer later improved this bound to log 6/g. The braids in this paper give rise to mapping classes with dilatations bounded above by log(2+sqrt(3))/g. They show that least dilatations for hyperelliptic mapping classes have the same asymptotic behavior as for general mapping classes on genus-g surfaces. | |
| dc.description | This is the version published by Algebraic & Geometric Topology on 12 June 2006 | |
| dc.identifier | https://arxiv.org/abs/0904.0594 | |
| dc.identifier | http://arxiv.org/abs/0904.0594 | |
| dc.identifier | Algebr. Geom. Topol. 6 (2006) 699-738 | |
| dc.identifier | doi:10.2140/agt.2006.6.699 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/225813 | |
| dc.subject | Geometric Topology | |
| dc.subject | 37E30, 57M50 | |
| dc.title | A family of pseudo-Anosov braids with small dilatation | |
| dc.type | text |