자료유형  

 학위논문

Control Number  

0017163562

International Standard Book Number  

9798384467014

Dewey Decimal Classification Number  

510

Main Entry-Personal Name  

Sridhar, Shruthi.

Publication, Distribution, etc. (Imprint  

[S.l.] : Princeton University., 2024

Publication, Distribution, etc. (Imprint  

Ann Arbor : ProQuest Dissertations & Theses, 2024

Physical Description  

104 p.

General Note  

Source: Dissertations Abstracts International, Volume: 86-04, Section: B.

General Note  

Advisor: Gabai, David.

Dissertation Note  

Thesis (Ph.D.)--Princeton University, 2024.

Summary, Etc.  

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).

Subject Added Entry-Topical Term  

Mathematics.

Subject Added Entry-Topical Term  

Theoretical mathematics.

Index Term-Uncontrolled  

Configuration spaces

Index Term-Uncontrolled  

Embedding calculus

Index Term-Uncontrolled  

Embedding spaces

Index Term-Uncontrolled  

Homotopy groups

Index Term-Uncontrolled  

Spectral sequence

Added Entry-Corporate Name  

Princeton University Mathematics

Host Item Entry  

Dissertations Abstracts International. 86-04B.

Electronic Location and Access  

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Control Number  

joongbu:655671