[Binghamton Geometry/Topology Seminar] Feb 2 (the first seminar this semester)

[Dmytro Savchuk]

                   BINGHAMTON GEOMETRY/TOPOLOGY SEMINAR

*Date:*  Thursday, Feb 2, 2012

*Time:*  2:50-3:50pm
*Place:*  Library North 2205 followed by coffee/tea in the Anderson Reading
Room.

*Speaker:* Jean Sun* *(Yale University)
*Title: *Growth, Projections and Bounded Generation of Mapping Class Groups
*
Abstract:* We investigate the non-bounded generation of subgroups of
mapping class groups through the hierarchy in curve complexes developed by
Masur and Minsky (2000). We compare the subsurface projections to nearest
point projections in curve complexes and extend Behrstock's inequality to
include geodesics in curve complexes of subsurfaces in the Inequality on
Triples in Bestivina-Bromberg-Fujiwara (2010). Based on this inequality, we
can estimate translation lengths of words in the form $g_1^{n_1}\cdots
g_k^{n_k}$ when $\sum|n_k|$ is sufficiently large for any given sequence
$(g_i)_1^k$ in a mapping class group. With a growth argument, we further
show that any subgroup of a mapping class group is boundedly generated if
and only if it is virtually abelian.
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