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Families of Arcs in 4-Manifolds and Maps of Configuration Spaces
Families of Arcs in 4-Manifolds and Maps of Configuration Spaces
상세정보
- 자료유형
- 학위논문 서양
- 최종처리일시
- 20250211152724
- ISBN
- 9798384467014
- DDC
- 510
- 서명/저자
- Families of Arcs in 4-Manifolds and Maps of Configuration Spaces
- 발행사항
- [Sl] : Princeton University, 2024
- 발행사항
- Ann Arbor : ProQuest Dissertations & Theses, 2024
- 형태사항
- 104 p
- 주기사항
- Source: Dissertations Abstracts International, Volume: 86-04, Section: B.
- 주기사항
- Advisor: Gabai, David.
- 학위논문주기
- Thesis (Ph.D.)--Princeton University, 2024.
- 초록/해제
- 요약In this thesis we construct 3-parameter families G(p, q, r) of embedded arcs with fixed boundary in a 4-manifold. We then analyze these elements of π3Emb∂(I, M) using embedding calculus by studying the induced map from the embedding space to "Taylor approximations" TkEmb∂(I, M). We develop a diagrammatic framework inspired by cubical ω-groupoids to depict G(p, q, r) and related homotopies. We use this framework extensively in Chapter 4 to show explicitly that G(p, q, r) is trivial in π3T3Emb∂(I, M) (however, we conjecture that it is non-trivial in π3T4Emb∂(I, M)). In Chapter 5 we use the Bousfield-Kan spectral sequence for homotopy groups of cosimplicial spaces to show that the rational homotopy group π Q3 Emb∂(I, S1 x B3 ) is Q. This thesis extends work by Budney and Gabai in [BG21] which proves analogous results for π2Emb∂(I, M).
- 일반주제명
- Mathematics
- 일반주제명
- Theoretical mathematics
- 키워드
- Embedding spaces
- 키워드
- Homotopy groups
- 기타저자
- Princeton University Mathematics
- 기본자료저록
- Dissertations Abstracts International. 86-04B.
- 전자적 위치 및 접속
- 로그인 후 원문을 볼 수 있습니다.
MARC
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■020 ▼a9798384467014
■035 ▼a(MiAaPQ)AAI31490027
■040 ▼aMiAaPQ▼cMiAaPQ
■0820 ▼a510
■1001 ▼aSridhar, Shruthi.▼0(orcid)0000-0003-3975-8137
■24510▼aFamilies of Arcs in 4-Manifolds and Maps of Configuration Spaces
■260 ▼a[Sl]▼bPrinceton University▼c2024
■260 1▼aAnn Arbor▼bProQuest Dissertations & Theses▼c2024
■300 ▼a104 p
■500 ▼aSource: Dissertations Abstracts International, Volume: 86-04, Section: B.
■500 ▼aAdvisor: Gabai, David.
■5021 ▼aThesis (Ph.D.)--Princeton University, 2024.
■520 ▼aIn this thesis we construct 3-parameter families G(p, q, r) of embedded arcs with fixed boundary in a 4-manifold. We then analyze these elements of π3Emb∂(I, M) using embedding calculus by studying the induced map from the embedding space to "Taylor approximations" TkEmb∂(I, M). We develop a diagrammatic framework inspired by cubical ω-groupoids to depict G(p, q, r) and related homotopies. We use this framework extensively in Chapter 4 to show explicitly that G(p, q, r) is trivial in π3T3Emb∂(I, M) (however, we conjecture that it is non-trivial in π3T4Emb∂(I, M)). In Chapter 5 we use the Bousfield-Kan spectral sequence for homotopy groups of cosimplicial spaces to show that the rational homotopy group π Q3 Emb∂(I, S1 x B3 ) is Q. This thesis extends work by Budney and Gabai in [BG21] which proves analogous results for π2Emb∂(I, M).
■590 ▼aSchool code: 0181.
■650 4▼aMathematics
■650 4▼aTheoretical mathematics
■653 ▼aConfiguration spaces
■653 ▼aEmbedding calculus
■653 ▼aEmbedding spaces
■653 ▼aHomotopy groups
■653 ▼aSpectral sequence
■690 ▼a0405
■690 ▼a0642
■71020▼aPrinceton University▼bMathematics.
■7730 ▼tDissertations Abstracts International▼g86-04B.
■790 ▼a0181
■791 ▼aPh.D.
■792 ▼a2024
■793 ▼aEnglish
■85640▼uhttp://www.riss.kr/pdu/ddodLink.do?id=T17163562▼nKERIS▼z이 자료의 원문은 한국교육학술정보원에서 제공합니다.
