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The borders of Outer space

Presented by: 
Karen Vogtmann University of Warwick, Cornell University
Date: 
Friday 23rd June 2017 - 14:30 to 15:30
Venue: 
INI Seminar Room 1
Abstract: 
Outer space is an analog for the group Out(F_n) of the symmetric space associated to an algebraic group.  Motivated by work of Borel and Serre, 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. We realize this bordification as a deformation retract of Outer space instead of an extension.  We use this to give a simpler connectivity proof, and to give a description of the boundary nicely analogous to that of the Borel-Serre boundary of a symmetric space. This is joint work with Kai-Uwe Bux and Peter Smillie.
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons