Two- and three-cocycles for Laver tables
  We determine all 2- and 3-cocycles for Laver tables, an infinite sequence of finite structures obeying the left-selfdistributivity law; in particular, we describe simple explicit bases. This provides a number of new positive braid invariants and paves the way for further potential topological applications. Incidentally, we establish and study a partial ordering on Laver tables given by the right-divisibility relation. 
Patrick Dehornoy (LMNO, PPS), Victoria Lebed (OCAMI)
math.KT