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Lipshitz, Robert Gartner, Michael 2020-02-27T22:38:22Z 2020-02-27T22:38:22Z 2020-02-27 https://hdl.handle.net/1794/25283 Let Man* denote the category of closed, connected, oriented and based 3- manifolds, with basepoint preserving dieomorphisms between them. We show that the Heegaard Floer invariants yield functors from Man* to the category of transitive systems in the projectivized category of Z[U]-modules, whose values agree with the Heegaard Floer invariants dened by Ozsvath and Szabo. In doing so, we will see that these projective functors actually come from a transitive system, in the projectivized homotopy category of chain complexes over Z[U]-Mod, associated to each 3-manifold. This extends work of Juhasz, Thurston and Zemke, who showed that there are analogous functors coming from the Heegaard Floer invariants defined over F2. We discuss several applications of these naturality results, and use them to introduce and investigate an invariant of nonorientable 3-manifolds coming from Heegaard Floer Homology. This dissertation includes material that has been submitted for publication. en_US University of Oregon All Rights Reserved. Geometric Topology Heegaard Floer Homology Low Dimensional Topology Naturality in Heegaard Floer Homology Electronic Thesis or Dissertation Ph.D. doctoral Department of Mathematics University of Oregonopen.access