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3-Manifolds of S1-Category Three

Title: 3-Manifolds of S1-Category Three.
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Name(s): Wang, Dongxu, author
Heil, Wolfgang, professor directing thesis
Niu, Xufeng, university representative
Klassen, Eric P., committee member
Hironaka, Eriko, committee member
Nichols, Warren D., committee member
Department of Mathematics, degree granting department
Florida State University, degree granting institution
Type of Resource: text
Genre: Text
Issuance: monographic
Date Issued: 2013
Publisher: Florida State University
Florida State University
Place of Publication: Tallahassee, Florida
Physical Form: computer
online resource
Extent: 1 online resource
Language(s): English
Abstract/Description: I study 3-manifold theory, which is a fascinating research area in topology. Many new ideas and techniques were introduced during these years, which makes it an active and fast developing subject. It is one of the most fruitful branches of today's mathematics and with the solution of the Poincare conjecture, it is getting more attention. This dissertation is motivated by results about categorical properties for 3-manifolds. This can be rephrased as the study of 3-manifolds which can be covered by certain sets satisfying some homotopy properties. A special case is the problem of classifying 3-manifolds that can be covered by three simple S1-contractible subsets. S1-contractible subsets are subsets of a 3-manifold M3 that can be deformed into a circle in M3. In this thesis, I consider more geometric subsets with this property, namely subsets are homeomorphic to 3-balls, solid tori and solid Klein bottles. The main result is a classication of all closed 3-manifolds that can be obtained as a union of three solid Klein bottles.
Identifier: FSU_migr_etd-7650 (IID)
Submitted Note: A Dissertation submitted to the Department of Mathematics in partial fulfillment of the requirements for the degree of Doctor of Philosophy.
Degree Awarded: Summer Semester, 2013.
Date of Defense: Apri 4, 2013.
Bibliography Note: Includes bibliographical references.
Advisory Committee: Wolfgang Heil, Professor Directing Thesis; Xufeng Niu, University Representative; Eric P. Klassen, Committee Member; Eriko Hironaka, Committee Member; Warren D. Nichols, Committee Member.
Subject(s): Mathematics
Persistent Link to This Record: http://purl.flvc.org/fsu/fd/FSU_migr_etd-7650
Use and Reproduction: This Item is protected by copyright and/or related rights. You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s). The copyright in theses and dissertations completed at Florida State University is held by the students who author them.
Host Institution: FSU

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Wang, D. (2013). 3-Manifolds of S1-Category Three. Retrieved from http://purl.flvc.org/fsu/fd/FSU_migr_etd-7650