Naturality and Mapping Class Groups in Heegard Floer Homology Ronald M. Nowak sharks display many qualities we

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and an appendix with norms and scoring reference materials

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Naturality and Mapping Class Groups in Heegard Floer Homology Ronald M. Nowak sharks display many qualities weWe 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