Naturality and Mapping Class Groups in Heegard Floer Homology

Demonstrates that all versions of Heegaard Floer homology, link Floer homology, and sutured Floer homology are natural - they assign concrete groups to each based 3-manifold, based link, and balanced sutured manifold. Furthermore, the authors functorially assign isomorphisms to diffeomorphisms, and show that this assignment is isotopy invariant.