Presented by:
Gregory Arone
Date:
Tuesday 31st July 2018 - 15:30 to 16:30
Venue:
INI Seminar Room 2
Abstract:
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’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 that
our obstructions are closely related to Milnor invariants. When M is of
dimension 2 and d=4, we speculate that our obstructions are related to ones
constructed by Schneidermann and Teichner. This is very much work in progress.
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