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The Moduli Space of Singular Great Circle Fibrations of S3 and Their Dynamics- [electronic resource]
The Moduli Space of Singular Great Circle Fibrations of S3 and Their Dynamics- [electronic resource]
상세정보
- 자료유형
- 학위논문파일 국외
- 최종처리일시
- 20240214100124
- ISBN
- 9798379756024
- DDC
- 510
- 저자명
- Yang, Jingye.
- 서명/저자
- The Moduli Space of Singular Great Circle Fibrations of S3 and Their Dynamics - [electronic resource]
- 발행사항
- [S.l.]: : University of Pennsylvania., 2023
- 발행사항
- Ann Arbor : : ProQuest Dissertations & Theses,, 2023
- 형태사항
- 1 online resource(57 p.)
- 주기사항
- Source: Dissertations Abstracts International, Volume: 84-12, Section: B.
- 주기사항
- Includes supplementary digital materials.
- 주기사항
- Advisor: Gluck, Herman R.
- 학위논문주기
- Thesis (Ph.D.)--University of Pennsylvania, 2023.
- 사용제한주기
- This item must not be sold to any third party vendors.
- 초록/해제
- 요약How can a fiber bundle develop singularities? Perhaps some fibers move around and bump into one another so that they are no longer disjoint, while other fibers develop their own individual singularities. To separate these two phenomena from one another in a low-dimensional setting, we focus on fibrations of the three-sphere by great circles, insist that the fibers remain rigid, but allow them to drift and collide.To proceed quantitatively, we take advantage of a known moduli space for these fibrations, two copies of the family of strictly distance-decreasing mappings of a two-sphere to itself. The constant maps correspond to the Hopf fibrations and provide a homotopy-equivalent core consisting of two copies of a two-sphere. Then we view the singular fibrations as providing a boundary for this moduli space, in which the corresponding mappings are now only weakly distance-decreasing, though still of degree zero. We then• Prove that this enlarged moduli space retains its original homotopy type. • Provide a dynamic model for singularity formation, in which all the fibers bump into one another simultaneously. • Finally, we rely on the work of Kirszbraun, on the extension of Lipschitz maps between Hilbert spaces while preserving the Lipschitz constant, to prove that the smooth non-singular fibrations are dense in the enlarged space of possibly singular continuous fibrations.
- 일반주제명
- Mathematics.
- 일반주제명
- Theoretical mathematics.
- 일반주제명
- Applied mathematics.
- 키워드
- Fiber bundle
- 키워드
- Homotopy
- 키워드
- Lipschitz map
- 키워드
- Moduli space
- 기타저자
- University of Pennsylvania Mathematics
- 기본자료저록
- Dissertations Abstracts International. 84-12B.
- 기본자료저록
- Dissertation Abstract International
- 전자적 위치 및 접속
- 로그인 후 원문을 볼 수 있습니다.
MARC
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■00520240214100124
■006m o d
■007cr#unu||||||||
■020 ▼a9798379756024
■035 ▼a(MiAaPQ)AAI30424905
■040 ▼aMiAaPQ▼cMiAaPQ
■0820 ▼a510
■1001 ▼aYang, Jingye.
■24510▼aThe Moduli Space of Singular Great Circle Fibrations of S3 and Their Dynamics▼h[electronic resource]
■260 ▼a[S.l.]:▼bUniversity of Pennsylvania. ▼c2023
■260 1▼aAnn Arbor :▼bProQuest Dissertations & Theses, ▼c2023
■300 ▼a1 online resource(57 p.)
■500 ▼aSource: Dissertations Abstracts International, Volume: 84-12, Section: B.
■500 ▼aIncludes supplementary digital materials.
■500 ▼aAdvisor: Gluck, Herman R.
■5021 ▼aThesis (Ph.D.)--University of Pennsylvania, 2023.
■506 ▼aThis item must not be sold to any third party vendors.
■520 ▼aHow can a fiber bundle develop singularities? Perhaps some fibers move around and bump into one another so that they are no longer disjoint, while other fibers develop their own individual singularities. To separate these two phenomena from one another in a low-dimensional setting, we focus on fibrations of the three-sphere by great circles, insist that the fibers remain rigid, but allow them to drift and collide.To proceed quantitatively, we take advantage of a known moduli space for these fibrations, two copies of the family of strictly distance-decreasing mappings of a two-sphere to itself. The constant maps correspond to the Hopf fibrations and provide a homotopy-equivalent core consisting of two copies of a two-sphere. Then we view the singular fibrations as providing a boundary for this moduli space, in which the corresponding mappings are now only weakly distance-decreasing, though still of degree zero. We then• Prove that this enlarged moduli space retains its original homotopy type. • Provide a dynamic model for singularity formation, in which all the fibers bump into one another simultaneously. • Finally, we rely on the work of Kirszbraun, on the extension of Lipschitz maps between Hilbert spaces while preserving the Lipschitz constant, to prove that the smooth non-singular fibrations are dense in the enlarged space of possibly singular continuous fibrations.
■590 ▼aSchool code: 0175.
■650 4▼aMathematics.
■650 4▼aTheoretical mathematics.
■650 4▼aApplied mathematics.
■653 ▼aDifferential geometry
■653 ▼aFiber bundle
■653 ▼aHomotopy
■653 ▼aLipschitz map
■653 ▼aModuli space
■653 ▼aSingular fibration
■690 ▼a0405
■690 ▼a0642
■690 ▼a0364
■71020▼aUniversity of Pennsylvania▼bMathematics.
■7730 ▼tDissertations Abstracts International▼g84-12B.
■773 ▼tDissertation Abstract International
■790 ▼a0175
■791 ▼aPh.D.
■792 ▼a2023
■793 ▼aEnglish
■85640▼uhttp://www.riss.kr/pdu/ddodLink.do?id=T16931831▼nKERIS▼z이 자료의 원문은 한국교육학술정보원에서 제공합니다.
■980 ▼a202402▼f2024
