Skip to main content

Finding infinity inside Outer space

Posted in
Speaker: 
Karen Vogtmann
Zugehörigkeit: 
U of Warwick
Datum: 
Don, 09/06/2016 - 15:00 - 16:00
Location: 
MPIM Lecture Hall

The group Out(F_n) of outer automorphisms of a free group shares many properties with arithmetic
groups, although it is not even linear. The role of the symmetric space is played by a space known
as Outer space.  Motivated by work of Borel and Serre on arithmetic groups, Bestvina and Feighn
defined a bordification of Outer space; this is an enlargement of Outer space which is highly-connected
at infinity and on which the action of Out(F_n) extends with compact quotient; they are able to conclude
that Out(F_n) satisfies a type of duality between homology and cohomology.  I will describe Bestvina
and Feighn's  bordification  and show how to realize it as a deformation retract of Outer space instead
of an enlargement, answering some questions left open by Bestvina and Feighn and considerably
simplifying their proof that the bordification is highly connected at infinity.

© MPI f. Mathematik, Bonn Impressum & Datenschutz
-A A +A