Joining and gluing sutured Floer homology

Details Joining and gluing sutured Floer homology Joining and gluing sutured Floer homology

2010-10-18

arxiv.org/abs/1010.3496v1

Mathematics

Geometric Topology

58 pages, 46 figures

Scientific paper

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.

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