Homeomorphism groups represented by pairs of rooted trees

Liam Stott (University of St Andrews)

Monday 15th May, 2023 16:00-17:00 Maths 311B

Abstract

The elements of Thompson's group F can, famously, be represented as (equivalence classes of) pairs of binary rooted trees. In essence, this constructs F as a diagram group (in the sense of Guba & Sapir) and constitutes a fundamental example of such a group. Many natural modifications to this tree pair representation, giving rise to groups such as F_n, T and V, provide further fundamental examples of diagram groups; on the other hand, seemingly different tree pair representations may give rise to the same group. We will consider some examples, focusing on geometrically fast sets, which provide a natural class of such representations exemplifying these two extremes.

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