Naturality in Heegaard Floer Homology

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.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

doctoral

Discipline thesis:degree_discipline

Department of Mathematics

Grantor dc:publisher

University of Oregon

Year dc:date.issued

2020

Author dc:creator

• Gartner, Michael

Advisor dc:contributor.advisor

• Lipshitz, Robert

• Geometric Topology
• Heegaard Floer Homology
• Low Dimensional Topology

Statement dc:rights

• All Rights Reserved.

Language dc:language.iso

en_US

Handle dc:identifier.uri

https://hdl.handle.net/1794/25283

OAI record oai:identifier

https://scholarsbank.uoregon.edu/server/oai/request?verb=GetRecord&metadataPrefix=dim&identifier=oai%3Ascholarsbank.uoregon.edu%3A1794%2F25283