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Curve Complex Analogues for Out(F_n)

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Lucas Sabalka, Saint Louis University

What
  • Topology Seminar
When Fri, Sep 21, 2012
from 11:00 AM to 12:00 PM
Where Ritter Hall 316
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Abstract:  The group Out(F_n) of outer automorphisms of the free group has been an object of active study for many years, yet its geometry is not well understood.  Recently, effort has been focused on finding a hyperbolic complex on which Out(F_n) acts, in analogy with the curve complex for the mapping class group.  In this talk I will introduce these objects and discuss some results about the geometry of some proposed analogues.  I will focus on my joint work with Dmytro Savchuk on the geometry of the edge splitting graph, or equivalently the separating sphere graph.  We give a characterization of geodesic paths in this graph, and use our characterization to find lower bounds on distances between vertices.  Our distance calculations allow us to find quasiflats of arbitrary dimension.  Thus, this graph is not hyperbolic and has infinite asymptotic dimension.  I am planning on going slowly and giving definitions of unfamiliar concepts, so this will probably be a series of two talks.
 
 
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