BINGHAMTON GEOMETRY/TOPOLOGY SEMINAR<br><div class="gmail_quote"><div class="gmail_quote"><div> <br>Date: Thursday, November 4, 2010<br>Time: 2:50-3:50pm<br>Place: Library North 2205 followed by coffee/tea in the Anderson<br>
Reading Room.<br>
</div><div class="gmail_quote"> <br>Speaker: Dima Savchuk (Binghamton)<br>Title: Geometry of curve complex analogues for Out(F_n), I<br><br>Abstract: This is the first of two talks based on our joint work with Lucas Sabalka. One of the most popular open questions about Out(F_n) - a group of outer automorphisms of a free group of rank n - is the construction of a Gromov hyperbolic space on which Out(F_n) naturally acts, extending the deep analogy between Out(F_n), mapping class groups, and linear groups. Each mapping class group naturally acts on a curve complex of the surface, which is hyperbolic due to a celebrated theorem by Masur and Minsky. Many spaces which could serve as an analogue for this space were proposed in recent years. We will define some of them and concentrate mostly on a space named the ``Free factorization graph''. The main outcome of our work is that this space in not hyperbolic, so it should not be considered as an analogue to curve complex.<br>
<br>The first talk will be devoted to the background and introduction to the ideas and some techniques used in our proof.<br></div></div></div>