Invitation to the Logic Seminar at the National University of Singapore
Date: Thursday, 25 February 2016, 17:00 hrs
Room: S17#04-06, Department of Mathematics, NUS
Speaker: Andre Nies, The University of Auckland
Title: The complexity of isomorphism between profinite groups
A topological group G is profinite if it is compact and totally
disconnected. Equivalently, G is the inverse limit of a surjective
system of finite groups carrying the discrete topology. An example is
the additive group of 2-adic integers.
We discuss how to represent a countably based profinite group as a
point in a Polish space. Thereafter, we study the complexity of their
isomorphism using the theory of Borel reducibility in descriptive set
theory. For topologically finitely generated groups this complexity is
the same as the one of identity for reals. In general, it is the same
as the complexity of isomorphism for countable graphs.