University of Cambridge > Talks.cam > Isaac Newton Institute Seminar Series > Tree complexes and obstructions to embeddings.

Tree complexes and obstructions to embeddings.

Add to your list(s) Download to your calendar using vCal

If you have a question about this talk, please contact info@newton.ac.uk.

HHH - Homotopy harnessing higher structures

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.




This talk is part of the Isaac Newton Institute Seminar Series series.

Tell a friend about this talk:

This talk is included in these lists:

Note that ex-directory lists are not shown.

 

© 2006-2020 Talks.cam, University of Cambridge. Contact Us | Help and Documentation | Privacy and Publicity