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The borders of Outer space

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NPCW05 - Group actions and cohomology in non-positive curvature

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.

This talk is part of the Isaac Newton Institute Seminar Series series.

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