Abstract. Using contact-geometric techniques and sutured Floer homology, we present an alternate formulation of the minus and plus version of knot Floer homology. We further show how natural constructions in the realm of contact geometry give rise to much of the formal structure relating the various versions of Heegaard Floer homology.
We give a partial characterization of bordered Floer homology in terms of sutured Floer homology. The bordered algebra and modules are direct sums of certain sutured Floer complexes. The algebra multiplication and algebra action correspond to a new gluing map on SFH. It is defined algebraically, and is a special case of a more general "join" map.In a follow-up paper we show that this gluing map can be identified with the contact cobordism map of Honda-Kazez-Matić. The join map is conjecturally equivalent to the cobordism maps on SFH defined by Juhász.
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