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ON THE HOMOTOPY CLASS OF 2-PLANE FIELDS AND ITS APPLICATIONS IN
CONTACT TOPOLOGY
by
Yang Huang
A Dissertation Presented to the
FACULTY OF THE USC GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(MATHEMATICS)
August 2012
Copyright 2012 Yang Huang
Object Description
| Title | On the homotopy class of 2-plane fields and its applications in contact topology |
| Author | Huang, Yang |
| Author email | huangyan@usc.edu;hymath@gmail.com |
| Degree | Doctor of Philosophy |
| Document type | Dissertation |
| Degree program | Mathematics |
| School | College of Letters, Arts And Sciences |
| Date defended/completed | 2012-05-14 |
| Date submitted | 2012-06-19 |
| Date approved | 2012-06-20 |
| Restricted until | 2012-06-20 |
| Date published | 2012-06-20 |
| Advisor (committee chair) | Honda, Ko |
| Advisor (committee member) |
Bonahon, Francis Kocer, Yilmaz |
| Abstract | The goal of this thesis is to study homotopy classes of oriented 2-plane fields in 3-manifolds and apply them to 3-dimensional contact topology. Using a generalized version of the Pontryagin-Thom construction, we compute the homotopy class of a bypass attachment. Based on this computation, we give a new proof to the classification theorem of overtwisted contact structures, originally due to Eliashberg, using convex surface theory. |
| Keyword | contact topology; 2-plane field; homotopy; bypass; overtwisted contact structure |
| Language | English |
| Part of collection | University of Southern California dissertations and theses |
| Publisher (of the original version) | University of Southern California |
| Place of publication (of the original version) | Los Angeles, California |
| Publisher (of the digital version) | University of Southern California. Libraries |
| Provenance | Electronically uploaded by the author |
| Type | texts |
| Legacy record ID | usctheses-m |
| Contributing entity | University of Southern California |
| Rights | Huang, Yang |
| Physical access | The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the author, as the original true and official version of the work, but does not grant the reader permission to use the work if the desired use is covered by copyright. It is the author, as rights holder, who must provide use permission if such use is covered by copyright. The original signature page accompanying the original submission of the work to the USC Libraries is retained by the USC Libraries and a copy of it may be obtained by authorized requesters contacting the repository e-mail address given. |
| Repository name | University of Southern California Digital Library |
| Repository address | USC Digital Library, University of Southern California, University Park Campus MC 7002, 106 University Village, Los Angeles, California 90089-7002, USA |
| Repository email | cisadmin@lib.usc.edu |
| Archival file | uscthesesreloadpub_Volume4/etd-HuangYang-892.pdf |
Description
| Title | Page 1 |
| Contributing entity | University of Southern California |
| Repository email | cisadmin@lib.usc.edu |
| Full text | ON THE HOMOTOPY CLASS OF 2-PLANE FIELDS AND ITS APPLICATIONS IN CONTACT TOPOLOGY by Yang Huang A Dissertation Presented to the FACULTY OF THE USC GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulfillment of the Requirements for the Degree DOCTOR OF PHILOSOPHY (MATHEMATICS) August 2012 Copyright 2012 Yang Huang |
