The Lubin-Tate Theory of Spectral Lie Algebras
Citation
Brantner, David Lukas Benjamin. 2017. The Lubin-Tate Theory of Spectral Lie Algebras. Doctoral dissertation, Harvard University, Graduate School of Arts & Sciences.Abstract
We use equivariant discrete Morse theory to establish a general technique in poset topology and demonstrate its applicability by computing various equivariant properties of the partition complex and related posets in a uniform manner. Our technique gives new and purely combinatorial proofs of results on algebraic and topological Andr\'{e}-Quillen homology.We then carry out a general study of the relation between monadic Koszul duality and unstable power operations. Finally, we combine our techniques to compute the operations which act on the homotopy groups K(n)-local Lie algebras over Lubin-Tate space.
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