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Higher enveloping algebras and configuration spaces of manifolds

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Speaker: 
Benjamin Knudsen
Affiliation: 
Harvard University
Date: 
Mon, 2017-02-13 11:45 - 12:15
Location: 
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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