Subgroups generated by two pseudo-Anosov elements in a mapping class group. II. Uniform bound on exponents

Details Subgroups generated by two pseudo-Anosov elements in a mapping class group. II. Uniform bound on exponents Subgroups generated by two pseudo-Anosov elements in a mapping class group. II. Uniform bound on exponents

2009-08-07

arxiv.org/abs/0908.0995v1

Mathematics

Geometric Topology

33 pages, 11 figures

Scientific paper

Let $S$ be a compact orientable surface, and $\Mod(S)$ its mapping class group. Then there exists a constant $M(S)$, which depends on $S$, with the following property. Suppose $a,b \in \Mod(S)$ are independent (i.e., $[a^n,b^m]\not=1$ for any $n,m \not=0$) pseudo-Anosov elements. Then for any $n,m \ge M$, the subgroup $$ is free of rank two, and convex-cocompact in the sense of Farb-Mosher. In particular all non-trivial elements in $$ are pseudo-Anosov. We also show that there exists a constant $N$, which depends on $a,b$, such that $$ is free of rank two and convex-cocompact if $|n|+|m| \ge N$ and $nm \not=0$.

Affiliated with

Also associated with

No associations

Rating

Subgroups generated by two pseudo-Anosov elements in a mapping class group. II. Uniform bound on exponents 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 Subgroups generated by two pseudo-Anosov elements in a mapping class group. II. Uniform bound on exponents, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Subgroups generated by two pseudo-Anosov elements in a mapping class group. II. Uniform bound on exponents will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-152961