Gomez, Daniel
(2015)
A COUNTEREXAMPLE TO THE SIMPLE LOOP CONJECTURE FOR THE PUNCTURED KLEIN BOTTLE IN PGL(2,R).
Master's Thesis, University of Pittsburgh.
(Unpublished)
Abstract
In this paper, inspired by the work of Katherine Mann, we show a counterexample to the simple loop conjecture for a representation of the surface group of the punctured Klein bottle, K, in PGL(2,R). In the process, we provide an explicit description of the mapping class group, as well as a classification of possible simple closed curves on K.
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Details
| Item Type: |
University of Pittsburgh ETD
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| Status: |
Unpublished |
| Creators/Authors: |
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| ETD Committee: |
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| Date: |
8 June 2015 |
| Date Type: |
Publication |
| Defense Date: |
15 April 2015 |
| Approval Date: |
8 June 2015 |
| Submission Date: |
17 April 2015 |
| Access Restriction: |
No restriction; Release the ETD for access worldwide immediately. |
| Number of Pages: |
22 |
| Institution: |
University of Pittsburgh |
| Schools and Programs: |
Dietrich School of Arts and Sciences > Mathematics |
| Degree: |
MS - Master of Science |
| Thesis Type: |
Master's Thesis |
| Refereed: |
Yes |
| Uncontrolled Keywords: |
algebra, topology, simple, loop, conjecture, punctured, Klein, bottle, counterexample, representation, SL(2,R), PGL(2,R), mapping, class, group, surface, diffeomorphism, simple, closed, curve, classification |
| Date Deposited: |
08 Jun 2015 16:13 |
| Last Modified: |
15 Nov 2016 14:27 |
| URI: |
http://d-scholarship.pitt.edu/id/eprint/24948 |
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