A Product on Double Cosets of $B_\infty$

Pablo Gonzalez Pagotto

Institut Fourier, Université Grenoble Alpes, Grenoble, France

Abstract: For some infinite-dimensional groups $G$ and suitable subgroups $K$ there exists a monoid structure on the set $K\backslash G/K$ of double cosets of $G$ with respect to $K$. In this paper we show that the group $B_\infty$, of the braids with finitely many crossings on infinitely many strands, admits such a structure.

Keywords: Braid group; double cosets; Burau representation.

MSC: 20F36; 20M99; 20C99

Received: May 28, 2018; in final form December 14, 2018; Published online December 27, 2018

Language: English

DOI: 10.3842/SIGMA.2018.134

Bibliographic databases:

• 
• 

ArXiv: 1804.09603