Tuesday, September 7
Lucas Sabalka, Binghamton University
The group Out(Fn) of outer automorphisms of the free group has been an object of active study for many years, yet its geometry is not well understood. Recently, effort has been focused on finding a hyperbolic complex on which Out(Fn) acts, in analogy with the curve complex for the mapping class group. In this talk on joint research with Dima Savchuk, we'll discuss some results about the geometry of free splitting graph, a space on which Out(Fn) acts and a proposed candidate for a curve complex analogue. In particular, we have found arbitrary rank quasi-flats in the free splitting graph, showing it is not hyperbolic and has infinite asymptotic dimension. Thus, it is probably not the `correct' curve complex analogue.
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