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Dissertation/Thesis Abstract

Involutive Heegaard Floer Homology and Homology Cobordism
by Dai, Irving, Ph.D., Princeton University, 2019, 112; 13882762
Abstract (Summary)

In this thesis, we present several results regarding the application of Heegaard Floer theory to the homology cobordism group. The majority of our work is concerned with giving a structural understanding of the involutive Heegaard Floer homology for linear combinations of Seifert fibered spaces. As an application, we show that if Y is a linear combination of Seifert fibered homology spheres with μ(Y) = 1, then Y is not torsion in the homology cobordism group. We also discuss what can be said about the Pin(2)-equivariant monopole Floer homology of Seifert fibered spaces using our techniques. These results give a possible approach towards showing that Seifert fibered spaces do not generate the homology cobordism group.

Indexing (document details)
Advisor: Szabo, Zoltan
Commitee: Gabai, David, Ozsvath, Peter
School: Princeton University
Department: Mathematics
School Location: United States -- New Jersey
Source: DAI-B 80/11(E), Dissertation Abstracts International
Subjects: Theoretical Mathematics
Keywords: Floer theory, Low-dimensional topology
Publication Number: 13882762
ISBN: 978-1-392-26975-6
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