[Binghamton Geometry Topology Seminar] Geometry and Topology seminar: Collin Bleak

[Cary Malkiewich]

Hi everyone,

This week we are pleased to have Collin Bleak (University of St Andrews)
speaking about Thompson's group V, title and abstract below. This will be a
*hybrid* talk, which you can attend either in-person on Thursday at 2:50pm
in WH 100E, or online at the link:

https://binghamton.zoom.us/j/99386542764

We will also have a lunch social, meet at 12pm just outside WH100E. See you
there!

Best,
Cary

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Title: On the maximal subgroups of R. Thompson's group *V*

Abstract: The maximal subgroups of various groups have been a focus of
study since the highly influential O'Nan--Scott Theorem of 1979, which
classified the maximal subgroups of the finite symmetric groups. Motivated
by our perspective on R. Thompson's group *V *as a natural generalisation
of the finite symmetric and alternating groups to an infinite context, we have
been exploring the maximal subgroup structure of* V*, working to move
beyond the previously known maximal subgroups: the automorphic images
of *T* and
the set-wise stabilisers of finite sets of points in Cantor space (all with
the same tail class).

  We introduce the concept of a type system *P*, that is, a partition on
the set of finite words over the alphabet *{0,1}* compatible with the
partial action of Thompson's group *V*, and associate a subgroup *Stab_V(P)*
 of *V*. We classify the finite simple type systems and show that the
stabilizers of various simple type systems, including all finite simple
type systems, are maximal subgroups of *V*.  A biproduct of our approach is
that we can specify an uncountable family of pairwise non-isomorphic
maximal subgroups of *V*.

Joint with Jim Belk, Martyn Quick, and Rachel Skipper.
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