2003/10/27 by Kai-Uwe Bux, Bux, Kai-Uwe
Mathematics · #20F65 #Combinatorics (math.CO) #FOS: Mathematics #Geometric Topology (math.GT) #math.CO #math.GT #msc:20F65
paper · pdf · doi:10.48550/arxiv.math/0310420
19 pages, 8 figures
arxiv created 2003/10/27 · arxiv updated 2009/12/01
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.