[Binghamton Geometry/Topology Seminar] Mar 15

[Dmytro Savchuk]

                 BINGHAMTON GEOMETRY/TOPOLOGY SEMINAR

*Date:*  Thursday, Mar 15, 2012

*Time:*  2:50-3:50pm
*Place:*  Library North 2205 followed by coffee/tea in the Anderson Reading
Room.

*Speaker: ** *Yael Algom Kfir (Yale University)
*Title: *The metric completion of Outer Space
 *
Abstract:* Out(F_n) acts naturally on several geometric objects. There is a
proper isometric action on Outer Space which plays the role of a
homogeneous space of the Lie group in our setting. There are also several
simplicial complexes with natural Out(F_n) actions. Three important
examples are: the free factor complex - which was recently shown to be
Gromov hyperbolic (Bestvina-Feighn), the separating splitting complex -
which has quasi-flats of unbounded rank (Sabalka-Savchuk), and the free
splitting complex - which even more recently was shown to be Gromov
hyperbolic (Handel-Mosher). It is still not fully understood how these
complexes relate to each other and to Outer Space. I will present a proof
that the free splitting complex is homeomorphic to the simplicial  part of
the metric completion of Outer Space. As an application, I will present a
new proof of a theorem of Francaviglia-Martino: The isometry group of Outer
Space is Out(F_n) for n \geq 3 and PGL(2,Z) for n=2.
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