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Higher enveloping algebras and configuration spaces of manifolds

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Benjamin Knudsen
Harvard University
Mon, 13/02/2017 - 11:45 - 12:15
MPIM Lecture Hall

I will describe a construction providing Lie algebras with enveloping algebras over the operad of little $n$-dimensional
disks for any $n$. These algebras enjoy a combination of good formal properties and computability, the latter afforded
by a Poincaré-Birkhoff-Witt type result. The main application pairs this theory with the theory of factorization homology
in a study of the rational homology of configuration spaces, leading to a wealth of computations, improvements of classical results, and a combinatorial proof of homological stability.

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