Osaka University

Wed 11 Mar 2015, 3:15pm
Topology and related seminars
ESB 4133

PseudoAnosovs with small dilatations in the hyperelliptic handlebody groups and spherical Hilden groups

ESB 4133
Wed 11 Mar 2015, 3:15pm4:15pm
Abstract
This is a joint work with Susumu Hirose. We consider pseudoAnosov elements of the mapping class groups on orientable surfaces. We are interested in a numerical invariant of pseudoAnosovs, called the dilatation. The logarithm of the dilatation of a pseudoAnosov mapping class is called the entropy. If we fix a surface, then the set of dilatations of pseudoAnosovs defined on the surface is closed and discrete. In particular we can talk about a minimum of any subset of dilatations defined on the surface in question.
Penner proved that the minimal entropy of pseudoAnosovs defined on a closed surface of genus g behaves like 1/g. Later Hironaka proved that the minimal entropy of pseudoAnosovs in the handlebody subgroup on a closed surface of genus g also behaves like 1/g. We prove that the the minimal entropy of the hyperelliptic handlebody sugbroup of genus g has the same asymptotic behavior. (Our examples of pseudoAnosovs improve the upper bound of the minimal entropy of the handlebody sugbroup given by Hironaka.) To do this, we study the spherical Hilden subgroup of the mapping class group defined on a sphere with 2n punctures, and we construct a sequence of pseudoAnosovs with small dilatations in the spherical Hilden subgroups.
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UBC

Tue 17 Mar 2015, 2:00pm
SPECIAL
Topology and related seminars
ESB 4133


ESB 4133
Tue 17 Mar 2015, 2:00pm3:00pm
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UBC

Wed 25 Mar 2015, 3:15pm
Topology and related seminars
ESB 4133


ESB 4133
Wed 25 Mar 2015, 3:15pm4:15pm
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