Presentations for Brin’s higher-dimensional Thompson groups nV

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• Martyn Quick (St Andrews)
• Wednesday 04 December 2019, 16:30-17:30
• MR12.

If you have a question about this talk, please contact Christopher Brookes.

In 2004, Brin introduced, for each integer n >= 2, a group nV consisting of certain homeomorphisms of n-dimensional Cantor space. This generalises the group V defined by Richard Thompson in 1965 and provides further examples of finitely presented infinite simple groups.  In this talk, I will describe recent work that gives new presentations for each of the groups nV obtained by exploiting transpositions of disjoint basic open sets.  The first presentation is infinite, is analogous to the Coxeter presentation for the finite symmetric group and reflects the self-similar structure of Cantor space.  The second is a reduction to a finite presentation that is considerably smaller than those previously known.

This talk is part of the Algebra and Representation Theory Seminar series.

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