  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.
