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Leininger, Christopher J. Dunfield, Nathan Kapovich, Ilya Schupp, Paul Mousley, Sarah C. 2019-08-23T19:51:43Z 2019-08-23T19:51:43Z 2019-04-10 2019-05 Although the hierarchically hyperbolic space boundary is a generalization of the Gromov boundary, we will show there are fundamental differences between the two. First, we provide negative answers to questions posed by Durham, Hagen, and Sisto on the existence of boundary maps for some hierarchically hyperbolic spaces, namely maps from right-angled Artin groups to mapping class groups. We then answer another question of Durham, Hagen, and Sisto, proving that a Teichmuller geodesic ray does not necessarily converge to a unique point in the hierarchically hyperbolic space boundary of Teichmuller space. In fact, we prove that the limit set can be almost anything allowed by the topology. Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2019-08-22 without embargo terms The student, Sarah Mousley, accepted the attached license on 2019-04-08 at 14:21. The student, Sarah Mousley, submitted this Dissertation for approval on 2019-04-08 at 21:09. This Dissertation was approved for publication on 2019-04-10 at 14:40. DSpace SAF Submission Ingestion Package generated from Vireo submission #13520 on 2019-08-22 at 14:41:56 Made available in DSpace on 2019-08-23T19:51:43Z (GMT). No. of bitstreams: 12 MOUSLEY-DISSERTATION-2019.pdf: 678655 bytes, checksum: f0b1aa8531e5175fd16ddbe41d6bdb9a (MD5) Mousley_thesis.tex: 9122 bytes, checksum: 185030a96b59c8eebd8365a4e1b48a3a (MD5) abs.tex: 699 bytes, checksum: cbe6422dab37a17d8340d4cc237bde89 (MD5) acknowledgments.tex: 1959 bytes, checksum: fd041d4292070822c43784ce0355ef1b (MD5) background.tex: 33473 bytes, checksum: 3e7b9757da95bf584a3f55b6a3aa9ebd (MD5) exotic_limit_sets.tex: 51795 bytes, checksum: 8a2b460d845f9909dcd013f34d2fcf30 (MD5) intro.tex: 17126 bytes, checksum: c778c4f176a884a5ebea41b4dd2add6b (MD5) non_existence_boundary_maps.tex: 72543 bytes, checksum: ac1f1484d2e5287e9f5d36ea5639c766 (MD5) symbollist.tex: 1169 bytes, checksum: b434508ac7fc2c346d7e1fc04cca9d3d (MD5) thesisrefs.bib: 43051 bytes, checksum: d8a8816421e3c0a348363578e1927f35 (MD5) LICENSE.txt: 4210 bytes, checksum: c72c0136850c17992d94e8fd300b6ca7 (MD5) PROQUEST_LICENSE.txt: 4556 bytes, checksum: 5ba13498b8414379e0a8d4ec896d487d (MD5) Previous issue date: 2019-04-10 application/pdf http://hdl.handle.net/2142/104790 en Copyright 2019 Sarah Camille Mousley Mackay Teichmuller space mapping class group right-angled Artin group hierarchically hyperbolic limit set Boundaries and hierarchically hyperbolic spaces text text Mathematics Mathematics University of Illinois at Urbana-Champaign Dissertation Ph.D.