  We describe a series of complexes that relate to the braid groups as the
matching complexes relate to the symmetric groups. A modified construction
applies as well to other complexes based on edge sets in graphs. We show that
our constructions will yield Cohen-Macauley complexes provided the underlying
complexes are Cohen-Macauley.
  Finally, we discuss a related series of complexes to provide some positive
evidence that the braided Houghton groups, introduced by F. Degenhardt, are a
series of groups with linearly increasing finiteness length as are the
(unbraided) Houghton groups.
