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SUMMARY:Tree complexes and obstructions to embeddings. - Gregory Arone (St
 ockholm University)
DTSTART:20180731T143000Z
DTEND:20180731T153000Z
UID:TALK108523@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:Using the framework of the calculus of functors (a combination
  of manifold and orthogonal calculus) we define a sequence of obstructions
  for embedding a smooth manifold (or more generally a CW complex) M in R^d
 . The first in the sequence is essentially Haefliger&rsquo\;s obstruction.
  The second one was studied by Brian Munson. We interpret the n-th obstruc
 tion as a cohomology of configurations of n points on M with coefficients 
 in the homology of a complex of trees with n leaves. The latter can be ide
 ntified with the cyclic Lie_n representation. When M is a union of circles
 \, we conjecture that our obstructions are closely related to Milnor invar
 iants. When M is of dimension 2 and d=4\, we speculate that our obstructio
 ns are related to ones constructed by Schneidermann and Teichner. This is 
 very much work in progress.<br><br><br><br><br>
LOCATION:Seminar Room 2\, Newton Institute
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