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SUMMARY:Cycles in moduli spaces of graphs - Karen Vogtmann\, Cornell
DTSTART:20150304T160000Z
DTEND:20150304T170000Z
UID:TALK56058@talks.cam.ac.uk
CONTACT:Ivan Smith
DESCRIPTION:Moduli spaces of finite metric graphs paramaterize many\npheno
 mena in science and mathematics.  In this talk I will discuss the\ntopolog
 y of such spaces.  If the graphs have no univalent vertices the\nrational 
 cohomology of the moduli space is the cohomology of the group\nOut(F_n) of
  outer automorphisms of a free group.\nThis cohomology  vanishes in high a
 nd low\ndimensions\, but Euler characteristic calculations show that there
  must\nbe many classes in the middle range.    I will\nsummarize what we k
 now  and then show how tools from topology\,\nrepresentation theory and mo
 dular forms can be used to construct a\nlarge number of cocycles\; the ide
 a is to glue together cocycles from\nspaces of lower genus graphs with uni
 valent vertices.\nParts of this talk are based on recent joint work with\n
 J. Conant\, A. Hatcher and M. Kassabov.\n
LOCATION:MR13
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