## Geometry and Topology

•  Eiko Kin, Osaka University, Japan
•  A construction of pseudo-Anosov braids with small normalized entropies
•  05/07/2019
•  2:00 PM - 3:00 PM
•  C304 Wells Hall

We consider pseudo-Anosov braids b. The logarithm of the stretch factor of the pseudo-Anosov braid b is called the entropy. By normalized entropy of b with n strands, we mean the n times (the entropy of b). Let b_n be a sequence of pseudo-Anosov braids. We say that the sequence b_n has a small normalized entropy if the number of strands of b_n behaves like n and the normalized entropy of b_n is bounded from above by a constant which does not depend on n. We give a construction of sequences of pseudo-Anosov braids having small normalized entropies. As an application, we explain the smallest entropy among skew-palindromic braids with n strands is comparable to 1/n. This is joint work with Susumu Hirose.

## Contact

Department of Mathematics
Michigan State University