Asymptotic translation lengths of point-pushing pseudo-Anosovs on the curve complex

Geometry Topology Seminar
Monday, April 17, 2017 - 14:05
1 hour (actually 50 minutes)
Skiles 006
Morehouse College
Let S be a Riemann surface of type (p,1), p > 1.  Let f be a point-pushing pseudo-Anosov map of S.  Let t(f) denote the translation length of f on the curve complex for S.  According to Masur-Minsky, t(f) has a uniform positive lower bound c_p that only depends on the genus p.Let F be the subgroup of the mapping class group of S consisting of point-pushing mapping classes.  Denote by L(F) the infimum of t(f) for f in F pseudo-Anosov.  We know that L(F) is it least c_p.  In this talk we improve this result by establishing the inequalities .8 <= L(F) <= 1 for every genus p > 1.