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.
|Commitee:||Gabai, David, Ozsvath, Peter|
|School Location:||United States -- New Jersey|
|Source:||DAI-B 80/11(E), Dissertation Abstracts International|
|Keywords:||Floer theory, Low-dimensional topology|
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