Two- and three-cocycles for Laver tables

2014/01/10 by Patrick Dehornoy, Dehornoy, Patrick, Victoria Lebed +1
Mathematics · #Algebraic structures and combinatorial models #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT)

paper · pdf · doi:10.48550/arxiv.1401.2335

openalex publication_date 2014/01/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We determine all 2- and 3-cocycles for Laver tables, an infinite sequence of\nfinite structures obeying the left-selfdistributivity law; in particular, we\ndescribe simple explicit bases. This provides a number of new positive braid\ninvariants and paves the way for further potential topological applications.\nIncidentally, we establish and study a partial ordering on Laver tables given\nby the right-divisibility relation.\n

Citations

• A classifying invariant of knots, the knot quandle

Related

• Laver's results and low-dimensional topology
• The Braid Shelf
• Calculus of the first non-trivial 1-cocycle of the space of long knots
• Hechler and Laver Trees
• More 1-cocycles for classical knots