[Binghamton Geometry/Topology Seminar] Geometry/Topology Seminar

[Christoforos Neofytidis]

BINGHAMTON GEOMETRY/TOPOLOGY SEMINAR

   Date: Thursday, September 8th, 2016

   Time: 2.50 pm

   Place: Whitney Hall, Room 100E

   Speaker: Phillip Wesolek (SUNY at Binghamton)

   Title: Elementary amenable groups and the space of marked groups.

Abstract: (joint work with J. Williams.) The space of marked groups is a
compact totally disconnected space that parameterizes all countable
groups. This space allows for tools from descriptive set theory to be
applied to study group-theoretic questions. In this talk, we consider the
collection of elementary amenable marked groups. The class of elementary
amenable groups is the smallest class that contains the abelian groups and
the finite groups and that is closed under group extension, taking
subgroups, taking quotients, and taking countable  directed unions. We
give a characterization of elementary amenable groups in terms of a chain
condition. We then show the set of elementary amenable marked groups is
not in the Borel sigma algebra of the space of marked groups. This gives a
new, non-constructive proof of a theorem of Grigorchuk: There are finitely
generated amenable non-elementary amenable groups.

NOTE:  The seminar has a webpage where the semester's program is listed:

http://www2.math.binghamton.edu/p/seminars/topsem