Resumen de The group of parenthesized braids

Patrick Dehornoy

• We investigate a group B¿ that includes Artin's braid group B8 and Thompson's group F. The elements of B¿ are represented by braids diagrams in which the distances between the strands are not uniform and, besides the usual crossing generators, new rescaling operators shrink or stretch the distances between the strands. We prove that B¿ is a group of fractions, that it is orderable, admits a nontrivial self-distributive structure, i.e., one involving the law x(yz)=(xy)(xz), it embeds in the mapping class group of a sphere with a Cantor set of punctures, and that Artin's representation of B8 into the automorphisms of a free group extends to B¿.