Topology & Geometric Group Theory Seminar

Fall 2011

1:30 – 2:30, Malott 203

Tuesday, December 6

Camille Horbez , Cornell University (visiting from ENS)

Sphere paths in outer space

In order to study the group Out(Fn) of outer automorphisms of a finitely generated free group, it is worth looking at its action on a topological space called outer space, built as an analog of Teichmuller space. While the topology of outer space is quite well-understood, its geometry is far less. There is an asymmetric metric on outer space, and outer space is geodesic for this metric, the geodesics being constructed as 'folding paths'. In the talk, we will investigate the metric properties of another collection of paths in outer space, defined in terms of spheres in a 3-dimensional manifold, that look like 'unfolding paths'. In particular, we will provide an explicit description of these paths in rank two outer space.

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