Naturality in Heegaard Floer Homology
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Date
2020-02-27
Authors
Gartner, Michael
Journal Title
Journal ISSN
Volume Title
Publisher
University of Oregon
Abstract
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.
Description
Keywords
Geometric Topology, Heegaard Floer Homology, Low Dimensional Topology