[Binghamton Geometry/Topology Seminar] March 4

[Marco Varisco]

Binghamton Geometry/Topology Seminar
http://www.math.binghamton.edu/dept/topsem/

Date: Thursday, March 4, 2010

Time: 2:50-3:50 pm

Place: Library North 2205
(followed by coffee/tea in the Anderson Reading Room)

Speaker: Ross Geoghegan (Binghamton University)

Title: The fundamental group at infinity

Abstract: If X is a locally finite complex, is X a (non-trivial)
covering space? To refine the question, assume X has one end and
finite dimension. In a remarkable theorem published in 1992, David
Wright gave a necessary condition for X to be a covering space. As a
consequence, two old problems fell: neither (1) Whitehead's
contractible 3-manifold nor (2) the interior of a compact contractible
manifold whose boundary is not simply connected can be covering
spaces.
Wright's Theorem also has consequences for group theory, as it gives
information about “the fundamental group at infinity” of a finitely
presented group. I will state Wright's Theorem and then I'll present a
new improvement of it. This improved version has nice consequences in
both topology and group theory. (This improvement is joint work with
Craig Guilbault.)