School of Mathematics, Statistics and Physics

Seminar Item

Pure Maths (Algebra and Geometry) - Maria Cumplido (Universidad Complutense Madrid)

A new family of infinitely braided Thompson's groups

Date/Time: Monday 9 November, 1.30pm - Algebra and Geometry Seminar

Venue: Zoom

Abstract: 

There is a generalisation of Thompson's groups constructed from the Thompson's group V and Artin's braid group. The braided Thompson's group BV_2 was independently introduced  by Patrick Dehornoy and Matthew G. Brin in 2006. In this talk we will explain how two extend this concept to a much bigger family of groups by using infinite braids: Infinitely braided Thompson's groups BV_n(H), where H is a subgroup of the braid group on n strands. We will prove that they are indeed groups by using braided diagrams and rewriting systems. We will also see that they are finitely generated if H is finitely generated and give an explicit set of generators for BV_n(H) and some other cases. This is a joint work with Julio Aroca.