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Ribbon cobordisms:

Thesis advisor: Joshua E. Greene / We study ribbon cobordisms between 3-manifolds, i.e. rational homology cobordisms that admit a handle decomposition without 3-handles. We first define and study the more general notion of quasi-ribbon cobordisms, and analyze how lattice-theoretic methods may be used to obstruct the existence of a quasi-ribbon cobordism between two given 3-manifolds. Building on this and on previous work of Lisca, we then determine when there exists such a cobordism between two connected sums of lens spaces. In particular, we show that if an oriented rational homology sphere Y admitsa quasi-ribbon cobordism to a lens space, then Y must be homeomorphic to L(n, 1), up to orientation-reversal. As an application, we classify ribbon χ-concordances between connected sums of 2-bridge links. Lastly, we show that the notion of ribbon rational homology cobordisms yields a partial order on the set consisting of aspherical 3-manifolds and lens spaces, thus providing evidence towards a conjecture formulated by Daemi, Lidman, Vela-Vick and Wong. / Thesis (PhD) — Boston College, 2022. / Submitted to: Boston College. Graduate School of Arts and Sciences. / Discipline: Mathematics.

Identiferoai:union.ndltd.org:BOSTON/oai:dlib.bc.edu:bc-ir_109503
Date January 2022
CreatorsHuber, Marius
PublisherBoston College
Source SetsBoston College
LanguageEnglish
Detected LanguageEnglish
TypeText, thesis
Formatelectronic, application/pdf
RightsCopyright is held by the author, with all rights reserved, unless otherwise noted.

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