Mathematics Colloquia and Seminars
Finding infinity inside Outer spaceGeometry/Topology
|Speaker:||Karen Vogtmann, Cornell University/University of Warwick/MSRI|
|Start time:||Wed, Oct 5 2016, 3:10PM|
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.