Cycles in moduli spaces of graphs

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• Karen Vogtmann, Cornell
• Wednesday 04 March 2015, 16:00-17:00
• MR13.

If you have a question about this talk, please contact Ivan Smith.

Moduli spaces of finite metric graphs paramaterize many phenomena in science and mathematics. In this talk I will discuss the topology of such spaces. If the graphs have no univalent vertices the rational cohomology of the moduli space is the cohomology of the group Out(F_n) of outer automorphisms of a free group. This cohomology vanishes in high and low dimensions, but Euler characteristic calculations show that there must be many classes in the middle range. I will summarize what we know and then show how tools from topology, representation theory and modular forms can be used to construct a large number of cocycles; the idea is to glue together cocycles from spaces of lower genus graphs with univalent vertices. Parts of this talk are based on recent joint work with J. Conant, A. Hatcher and M. Kassabov.

This talk is part of the Differential Geometry and Topology Seminar series.

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