Towards topological applications of Laver tables

Abstract: Laver tables are certain finite shelves (i.e., sets endowed with a binary operation which is distributive with respect to itself). They originate from set theory and have a profound combinatorial structure. In this talk I will discuss our dreams regarding potential braid and knot invariant constructions using Laver tables, and also present some real results in this direction, such as a detailed description of 2- and 3-cocycles for Laver tables. The rich structure of the latter promises interesting topological applications.
(Joint work with Patrick Dehornoy)