Uniformly exponential growth and mapping class groups of surfaces

We show that the mapping class group (as well as closely related groups) of an orientable surface with finitely generated fundamental group has uniformly exponential growth. We further demonstrate the uniformly non-amenability of many of these groups.

Bibliographic Details
Main Authors: Anderson, J.W (Author), Aramayona, J. (Author), Shackleton, K.J (Author)
Format: Article
Language:English
Published: 2007.
Subjects:
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Description
Summary:We show that the mapping class group (as well as closely related groups) of an orientable surface with finitely generated fundamental group has uniformly exponential growth. We further demonstrate the uniformly non-amenability of many of these groups.