Naturality and Mapping Class Groups in Heegaard Floer Homology
By Andr'as Juh'asz, Dylan Thurston, Ian Zemke. Memoirs of the American Mathematical Society, 2012
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We show that all versions of Heegaard Floer homology, link Floer homology, and sutured Floer homology are natural. That is, they assign concrete groups to each based 3-manifold, based link, and balanced sutured manifold, respectively. Furthermore, we functorially assign isomorphisms to (based) diffeomorphisms, and show that this assignment is isotopy invariant. The proof relies on finding a simple generating set for the fundamental group of the “space of Heegaard diagrams,” and then showing that Heegaard Floer homology has no monodromy around these generators. In fact, this allows us to give sufficient conditions for an arbitrary invariant of multi-pointed Heegaard diagrams to descend to a natural invariant of 3-manifolds, links, or sutured manifolds.
Subfields: Geometry and Topology, Neurology
View Paper: https://www.semanticscholar.org/paper/2adcc899d37425effc00f750d2b5ddbf0ccfd083
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- Link cobordisms and absolute gradings in link Floer homology (2017, methodology): “ariant chain homotopy. A summary of the proof can be found in [Zem16, Proposition 3.5], though most of the details are due to other mathematicians, notably Ozsvath, Szabo, Juhasz and Thurston. See [JT12] for more on the question of naturality. We dene CFL1(Y;L;s) to be the collection of all of the c”