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Seminar: "The irrational-slope Thompson groups" (Pep Burillo, UPC)

Seminari Teoria de Grups 2016/2017, session 1

Date: Tuesday February 28th, 2017, 15:00 - 16:00 h.
Place: FME-UPC room S03
Speaker: Pep Burillo (Universitat Politecnica Catalunya)

Title: "The irrational-slope Thompson groups"

Abstract: In this talk we will introduce the irrational-slope Thompson groups. First described by Cleary in a 1995 paper, the groups use subdivisions of [0,1] in different lengths, using equations such as 1=x+x^2. Subdivision intervals have lengths x^n, and hence the slopes are also powers of x. The elements of the group admit interpretations as pairs of binary trees in pure Thompson style, with the only particularity of distinguishing the intervals given by each edge. We will take advantage of the tree interpretation to find expressions for the metric in the Cayley graph of the group, and also distortions of interesting subgroups.

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