|Location:||MSRI: Simons Auditorium|
In the study of Out(F_n), there are many different complexes that in some way generalize the curve complex for mapping class groups. This will be a working seminar to understand these different complexes, how they relate to each other, and why each one is useful.
Our goal is to understand the free splitting complex, the free factor complex, the cyclic splitting complex, the cosurface graph, the intersection graph, and any others we have time for. In particular, we’ll discuss hyperbolicity and homotopy type of the complexes, investigate the loxodromic, WPD, and contracting elements, and look at folding paths in some of the better known complexes. In addition, we’ll look at the maps between the complexes.