## Topology & Geometric Group Theory Seminar

## Fall 2010

### 1:30 – 2:30, Malott 253

Tuesday, September 7

**Lucas
Sabalka**, Binghamton University

*On the geometry of Out(F*_{n})

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 on joint
research with Dima Savchuk, we'll discuss some results about the
geometry of free splitting graph, a space on which Out(F_{n})
acts and a proposed candidate for a curve complex analogue. In
particular, we have found arbitrary rank quasi-flats in the free
splitting graph, showing it is not hyperbolic and has infinite
asymptotic dimension. Thus, it is probably not the `correct' curve
complex analogue.

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