## 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(F_{n}) 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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