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Leininger, Christopher J Dunfield, Nathan Bradlow, Steven Sadanand, Chandrika Loa, Christopher 2022-01-12T21:45:31Z 2022-01-12T21:45:31Z 2021-07-13 2021-08 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. Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2022-01-12 without embargo terms The student, Christopher Loa, accepted the attached license on 2021-07-09 at 10:30. The student, Christopher Loa, submitted this Dissertation for approval on 2021-07-09 at 10:37. This Dissertation was approved for publication on 2021-07-13 at 16:54. DSpace SAF Submission Ingestion Package generated from Vireo submission #16822 on 2022-01-12 at 12:44:34 Made available in DSpace on 2022-01-12T21:45:31Z (GMT). No. of bitstreams: 3 LOA-DISSERTATION-2021.pdf: 857077 bytes, checksum: 5118ef65b2f43ce16e2b520a3b2dfa2d (MD5) LICENSE.txt: 4212 bytes, checksum: 370c92e7af51beac460f5c073f322624 (MD5) PROQUEST_LICENSE.txt: 4558 bytes, checksum: 2567a8c64473b7fe3fc31d981638f373 (MD5) Previous issue date: 2021-07-13 application/pdf http://hdl.handle.net/2142/113005 en Copyright 2021 Christopher Loa geometry topology Free products of abelian groups in mapping class groups text Thesis Mathematics Mathematics University of Illinois at Urbana-Champaign Dissertation Ph.D.