On pseudo-Anosov maps, symplectic, Perron-Frobenius matrices, and compression bodies
- Degree Grantor:
- University of California, Santa Barbara. Mathematics
- Degree Supervisor:
- Darren Long
- Place of Publication:
- [Santa Barbara, Calif.]
- Publisher:
- University of California, Santa Barbara
- Creation Date:
- 2014
- Issued Date:
- 2014
- Topics:
- Mathematics
- Keywords:
- Perron-Frobenius,
Symplectic,
Pseudo-Anosov,
Dilatation,
Compression body, and
Mapping class group - Genres:
- Online resources and Dissertations, Academic
- Dissertation:
- Ph.D.--University of California, Santa Barbara, 2014
- Description:
In 1988, William Thurston announced the completion of a classification of surface automorphisms into three types up to isotopy: periodic, reducible, and pseudo-Anosov. The most common but also least understood maps in this classification are pseudo-Anosovs. We extend our understanding of pseudo-Anosov maps in two ways. First, we show that every Perron unit of appropriate degree has a power which appears as the spectral radius of a symplectic, Perron-Frobenius matrix. This is significant due to possible applications to understanding the spectrum of dilatations for a surface. Second, we present an alternative proof to an important result of Biringer, Johnson, and Minsky showing roughly that a power of a pseudo-Anosov extends over a compression body if and only if the stable lamination bounds. Our alternative proof follows ideas of Casson and Long first presented in 1985.
- Physical Description:
- 1 online resource (68 pages)
- Format:
- Text
- Collection(s):
- UCSB electronic theses and dissertations
- Other Versions:
- http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqm&rft_dat=xri:pqdiss:3682863
- ARK:
- ark:/48907/f3mc8x62
- ISBN:
- 9781321567359
- Catalog System Number:
- 990045117880203776
- Copyright:
- Robert Ackermann, 2014
- Rights:
In Copyright
- Copyright Holder:
- Robert Ackermann
File | Description |
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Access: Public access | |
Ackermann_ucsb_0035D_12472.pdf | pdf (Portable Document Format) |