A family of pseudo-Anosov braids with small dilatation

Details A family of pseudo-Anosov braids with small dilatation A family of pseudo-Anosov braids with small dilatation

2009-04-03

arxiv.org/abs/0904.0594v1

Algebr. Geom. Topol. 6 (2006) 699-738

Mathematics

Geometric Topology

This is the version published by Algebraic & Geometric Topology on 12 June 2006

Scientific paper

10.2140/agt.2006.6.699

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.

Affiliated with

Also associated with

No associations

Rating

A family of pseudo-Anosov braids with small dilatation does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with A family of pseudo-Anosov braids with small dilatation, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A family of pseudo-Anosov braids with small dilatation will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-151030