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. Abstract: 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! <http://math.huji.ac.il/amitsur.html> --------------------------------------------------------- Technion Math Net-2 (TECHMATH2) Editor: Michael Cwikel <techm@math.technion.ac.il> Announcement from: Gili Schul <gili.schul@mail.huji.ac.il>