Two- and three-cocycles for Laver tables

Patrick Dehornoy (1, 2) , Victoria Lebed (3)

1 LMNO - Laboratoire de Mathématiques Nicolas Oresme
2 PPS - Preuves, Programmes et Systèmes
3 OCAMI - Osaka City university Advanced Mathematical Institute [Osaka]

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.

Mots clés: selfdistributivity; Laver tables; rack cohomology; quandle cocycle invariants; right-divisibility ordering

Domaines: K-théorie et homologie [math.KT]

Patrick Dehornoy, Victoria Lebed. Two- and three-cocycles for Laver tables. 2014. ⟨hal-00926810v2⟩