Algebraic & Geometric Topology
- Algebr. Geom. Topol.
- Volume 6, Number 2 (2006), 699-738.
A family of pseudo-Anosov braids with small dilatation
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 strands determines a hyperelliptic mapping class with the same dilatation on a genus– surface. Penner showed that logarithms of least dilatations of pseudo-Anosov maps on a genus– surface grow asymptotically with the genus like , and gave explicit examples of mapping classes with dilatations bounded above by . Bauer later improved this bound to . The braids in this paper give rise to mapping classes with dilatations bounded above by . They show that least dilatations for hyperelliptic mapping classes have the same asymptotic behavior as for general mapping classes on genus– surfaces.
Algebr. Geom. Topol., Volume 6, Number 2 (2006), 699-738.
Received: 23 July 2005
Revised: 13 April 2006
Accepted: 26 April 2006
First available in Project Euclid: 20 December 2017
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Hironaka, Eriko; Kin, Eiko. A family of pseudo-Anosov braids with small dilatation. Algebr. Geom. Topol. 6 (2006), no. 2, 699--738. doi:10.2140/agt.2006.6.699. https://projecteuclid.org/euclid.agt/1513796542