Uniqueness of Morava K-theory

Details Uniqueness of Morava K-theory Uniqueness of Morava K-theory

2008-10-28

arxiv.org/abs/0810.5032v2

Mathematics

Algebraic Topology

16 pages. Minor modifications, to appear in Compositio Mathematica.

Scientific paper

We show that there is an essentially unique S-algebra structure on the Morava K-theory spectrum K(n), while K(n) has uncountably many MU or \hE{n}-algebra structures. Here \hE{n} is the K(n)-localized Johnson-Wilson spectrum. To prove this we set up a spectral sequence computing the homotopy groups of the moduli space of A-infinity structures on a spectrum, and use the theory of S-algebra k-invariants for connective S-algebras due to Dugger and Shipley to show that all the uniqueness obstructions are hit by differentials.

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