Joining and gluing sutured Floer homology

Abstract

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-Matic. The join map is conjecturally equivalent to the cobordism maps on SFH defined by Juhasz.

58 pages, 46 figures

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• Itsy bitsy topological field theory
• Peculiar modules for 4-ended tangles
• An enhanced Euler characteristic of sutured instanton homology
• Cornered Heegaard Floer homology
• Foliated Open Books
• Formal Contact Categories
• A friendly introduction to the bordered contact invariant
• Heegaard Floer Homologies: lecture notes