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SUMMARY:String topology and the configuration space of two points - Floria
 n Naef (Trinity College Dublin)
DTSTART:20221116T160000Z
DTEND:20221116T170000Z
UID:TALK189122@talks.cam.ac.uk
CONTACT:Oscar Randal-Williams
DESCRIPTION:String topology is the study of operations on the homology of 
 the free loop space LM for M a closed manifold. I will describe a model fo
 r (S^1-equivariant) string topology over the reals in terms of graph compl
 exes. The construction comes together with an action of a graphical model 
 for an approximation of the group of diffeomorphisms. From this we will be
  able to speculate how homotopy-invariant string topology is. Concretely\,
  we will see that string topology is not invariant in families\, by showin
 g that \\pi_*(aut(M)) does not preserve the string coproduct and picks up 
 an error term coming from a map \\pi_*(aut(M)) -> H_*(LM) that vanishes on
  \\pi_*(Diff(M)). Finally\, I will explain how this last part depends only
  on the configuration space of two points.\nThis is based on joint work wi
 th T. Willwacher.
LOCATION:MR13
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