The irrational-slope Thompson's groups

Abstract: José Burillo (Universitat Politècnica de Catalunya)

Title: The irrational-slope Thompson's groups

Abstract: Irrational-slope Thompson's groups were introduced by Cleary in two papers in 1995 and 2000, where he proved they are FP_\infty. These are groups of PL maps of [0,1] whose breakpoints are in some irrational subring of R and the slopes are also irrational numbers. Interest in these groups grew recently when it was asked whether they can be obtained as subgroups of Thompson's group F. In this paper we will introduce the golden ratio group F_\tau, describe how to work with it in terms of binary trees and also algebraically. We will show a presentation for F_\tau and show that elements admit a unique normal form, in similar fashion as F. We will study its metric properties and undistorted copies of F inside, and finally, if time permits, we will say a few words about the irrational versions of Thompson's groups T and V. This is joint work with Brita Nucinkis and Lawrence Reeves.

operator algebrasrings and algebras

Audience: researchers in the topic

Western Sydney University Abend Seminars

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