[Binghamton Geometry/Topology Seminar] Geometry &Topology Seminar

[somnath at math.binghamton.edu]

BINGHAMTON GEOMETRY/TOPOLOGY SEMINAR

*Date:*  Thursday, March 27th, 2013

*Time:*  2:50-3:50pm
*Place:*  Library North 2205 followed by coffee/tea in the Anderson
Reading Room.

*Speaker: ** *Collin Bleak (St. Andrews University)
*Title: * De Bruijn automorphisms of the full shift

*Abstract:*  We investigate a set of groups {SBC_n}. Each group SBC_n sits
very naturally in the full group of automorphisms of {0,1, ... , n-1}^Z,
the full shift on n letters, and is somehow a very natural object. Still,
the structure of each group SBC_n, at least initially, was quite a
mystery. These groups' elements are describable as finite transducers, and
so the groups SBC_n are linked strongly to the rational group R introduced
by Grigorchuk, Nekrashevych, and Suschanski. Furthermore, the group SBC_n
corresponds precisely to the outer automorphism group of the generalized
Higman-Thompson group G_{n,1} = V_n. In this talk, we exploit a connection
with De Bruijn graphs to begin to explore the structure of the groups
SBC_n. Amongst other results, we will show that for m \neq n, SBC_m is not
isomorphic to SBC_n, and we will also show that for n>2, the groups SBC_n
are infinite, locally finite groups (and hence are not finitely
generated). This talk features work from two separate projects involving
collaborators Y. Maissel, A. Navas, and P. Cameron.