Naturality and mapping class groups in Heegaard Floer homology

摘要: We show that all versions of Heegaard Floer homology, link and sutured homology are natural. That is, they assign concrete groups to each based 3-manifold, link, balanced manifold, respectively. Furthermore, we functorially isomorphisms (based) diffeomorphisms, this assignment is isotopy invariant. The proof relies on finding a simple generating set for the fundamental group "space diagrams," then showing has no monodromy around these generators. In fact, allows us give sufficient conditions an arbitrary invariant multi-pointed diagrams descend natural 3-manifolds, links, or manifolds.