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Leininger, Christopher Kapovich, Ilya Dunfield, Nathan Bradlow, Steven Li, Shixuan 2020-10-07T21:00:03Z 2020-10-07T21:00:03Z 2020-07-17 2020-08 For a pseudo-Anosov homeomorphism f on a closed surface of genus g greater of equals to 2, for which the entropy is on the order 1/g (the lowest possible order), Farb-Leininger-Margalit showed that the volume of the mapping torus is bounded, independent of g. We show that the analogous result fails for a surface of fixed genus g with n punctures, by constructing pseudo-Anosov homeomorphism with entropy of the minimal order (log n)/n, and volume tending to infinity. Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2020-10-02 without embargo terms The student, Shixuan Li, accepted the attached license on 2020-07-17 at 03:40. The student, Shixuan Li, submitted this Dissertation for approval on 2020-07-17 at 03:58. This Dissertation was approved for publication on 2020-07-17 at 17:07. DSpace SAF Submission Ingestion Package generated from Vireo submission #15671 on 2020-10-02 at 15:14:52 Made available in DSpace on 2020-10-07T21:00:03Z (GMT). No. of bitstreams: 3 LI-DISSERTATION-2020.pdf: 369849 bytes, checksum: c970683eb80250e6e2ba9ba7246fb22b (MD5) LICENSE.txt: 4207 bytes, checksum: f1da69843036d076d91c28d982667492 (MD5) PROQUEST_LICENSE.txt: 4553 bytes, checksum: 20dd4d7b1a8d260b30c77ea1af7b55f9 (MD5) Previous issue date: 2020-07-17 application/pdf http://hdl.handle.net/2142/108514 en Copyright 2020 by Shixuan Li. All rights reserved. pseudo-Anosovs volume punctured surfaces mapping torus Low dilatation pseudo-anosovs on punctured surfaces and volume text Thesis Mathematics Mathematics University of Illinois at Urbana-Champaign Dissertation Ph.D.