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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Tree complexes and obstructions to embeddings. - G
regory Arone (Stockholm University)
DTSTART;TZID=Europe/London:20180731T153000
DTEND;TZID=Europe/London:20180731T163000
UID:TALK108523AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/108523
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 essential
ly Haefliger&rsquo\;s obstruction. The second one
was studied by Brian Munson. We interpret the n-th
obstruction 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 identified with the cyclic Lie_n representation
. When M is a union of circles\, we conjecture tha
t our obstructions are closely related to Milnor i
nvariants. When M is of dimension 2 and d=4\, we s
peculate that our obstructions are related to ones
constructed by Schneidermann and Teichner. This i
s very much work in progress.
LOCATION:Seminar Room 2\, Newton Institute
CONTACT:INI IT
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