Two- and three-cocycles for Laver tables-Reference-Cited by-同舟云学术

Two- and three-cocycles for Laver tables

Published:2014-04 Issue:04 Volume:23 Page:1450017
ISSN:0218-2165
Container-title:Journal of Knot Theory and Its Ramifications
language:en
Short-container-title:J. Knot Theory Ramifications

Author:

Dehornoy Patrick¹²,Lebed Victoria³

Affiliation:

1. Laboratoire de Mathématiques Nicolas Oresme, UMR 6139 CNRS, Université de Caen, 14032 Caen, France

2. Laboratoire Preuves, Programmes, Systèmes, UMR 7126 CNRS, Université Paris-Diderot, 75205 Paris 13, France

3. OCAMI, Osaka City University, 3-3-138 Sugimoto, Sumiyoshi, Osaka, 558-8585, Japan

Abstract

We determine all 2- and 3-cocycles for Laver tables, an infinite sequence of finite structures obeying the left-self-distributivity 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. An important tool for constructing a combinatorially meaningful basis of 2-cocycles is the right-divisibility relation on Laver tables, which turns out to be a partial ordering.

Publisher

World Scientific Pub Co Pte Lt

Subject

Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218216514500175

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