Limits with braid arrangements
  We define a monoid structure on the set of $k$-equal arrangements and use this structure to define limits of braid arrangements. We compute the cohomology of the associated limits of rational models of the arrangements complex complements. We collect these complexes together into one complex by creating a new differential and product on their direct sum and show that the resulting complex is exact. 
Matthew S. Miller and Max Wakefield
math.AT math.CO