Hebrew University
Amitsur Algebra Seminar
Time: Thursday, Jan 5, 12:00-13:15

Place: math 209
Speaker: Yael Algom Kfir
Title: The completion of Outer Space.
The group of outer automorphisms of the free group, Out(F_n), acts
naturally on several geometric objects. It has an isometric action on
Outer Space which plays the role of a homogeneous space of a Lie group
in our setting. There are also several simplicial complexes with
natural Out(F_n) actions. Two important examples are the free factor
complex and the free splitting complex. Both complexes have recently
been shown to be Gromov hyperbolic (the free splitting complex by
Handel-Mosher and the free factor complex by Bestvina-Feighn). It is
still not yet 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.
You are cordially invited!
Technion Math Net-2 (TECHMATH2)
Editor: Michael Cwikel   <techm@math.technion.ac.il> 
Announcement from: Gili Schul   <gili.schul@mail.huji.ac.il>