Free products of abelian groups in mapping class groups
Loa, Christopher
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https://hdl.handle.net/2142/113005
Description
Title
Free products of abelian groups in mapping class groups
Author(s)
Loa, Christopher
Issue Date
2021-07-13
Director of Research (if dissertation) or Advisor (if thesis)
Leininger, Christopher J
Doctoral Committee Chair(s)
Dunfield, Nathan
Committee Member(s)
Bradlow, Steven
Sadanand, Chandrika
Department of Study
Mathematics
Discipline
Mathematics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
geometry
topology
Abstract
The notions of convex cocompactness and geometric finiteness originally come from the study of Kleinian groups. The analogous notion of convex cocompactness for mapping class groups is due to Farb-Mosher. In recent work, Dowdall-Durham-Leininger-Sisto have proposed a definition of “parabolic” geometric finiteness for mapping class groups. In this thesis, we construct a new family of examples of parabolically geometrically finite mapping class subgroups and prove that they are undistorted in Mod(S). We also prove that a subfamily of our examples are also geometrically finite in the sense of Durham-Hagen-Sisto.
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