Abstract

There is a close connection between the theory of Lie algebras and the study of additive invariants of configuration spaces of manifolds, which has been exploited in many calculations of rational homology. We begin the computational exploration of this connection away from characteristic zero, exhibiting a spectral sequence converging to the p-complete complex K-theory of configuration spaces—more generally, to their completed Morava E(co)homology—-and we identify its second page in terms of an algebraic homology theory for Lie algebras equipped with certain power operations. We construct a computationally accessible analogue of the classical Chevalley—Eilenberg complex for these Hecke Lie algebras, and we use it to perform a number of computations. This talk is based on joint work in progress with Lukas Brantner and Jeremy Hahn.