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Title: Involutive Heegaard Floer Homology and Homology Cobordism
Authors: Dai, Irving
Advisors: Szabo, Zoltan
Contributors: Mathematics Department
Keywords: Floer theory
Low-dimensional topology
Subjects: Theoretical mathematics
Issue Date: 2019
Publisher: Princeton, NJ : Princeton University
Abstract: 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 $\mu(Y) = 1$, 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.
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Type of Material: Academic dissertations (Ph.D.)
Language: en
Appears in Collections:Mathematics

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