A family of pseudo-Anosov braids with small dilatation

dc.creatorHironaka, Eriko
dc.creatorKin, Eiko
dc.date2009-04-03
dc.date.accessioned2026-07-07T13:00:19Z
dc.date.available2026-07-07T13:00:19Z
dc.descriptionThis 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.descriptionThis is the version published by Algebraic & Geometric Topology on 12 June 2006
dc.identifierhttps://arxiv.org/abs/0904.0594
dc.identifierhttp://arxiv.org/abs/0904.0594
dc.identifierAlgebr. Geom. Topol. 6 (2006) 699-738
dc.identifierdoi:10.2140/agt.2006.6.699
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/225813
dc.subjectGeometric Topology
dc.subject37E30, 57M50
dc.titleA family of pseudo-Anosov braids with small dilatation
dc.typetext

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