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Uniqueness of Morava K-theory

Part of: Homology and cohomology theories Categories with structure Operations and obstructions

Published online by Cambridge University Press:  27 September 2010

Vigleik Angeltveit
Vigleik Angeltveit*
Affiliation:
Department of Mathematics, University of Chicago, Chicago, IL 60637, USA (email: vigleik@math.uchicago.edu)
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Abstract

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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 $\widehat {E(n)}$-algebra structures. Here $\widehat {E(n)}$ 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∞ structures on a spectrum, and use the theory of S-algebra k-invariants for connectiveS-algebras found in the work of Dugger and Shipley [Postnikov extensions of ring spectra, Algebr. Geom. Topol. 6 (2006), 1785–1829 (electronic)] to show that all the uniqueness obstructions are hit by differentials.

Keywords

S-algebraMorava K-theorymoduli space

MSC classification

Secondary: 55N22: Bordism and cobordism theories, formal group laws 55S35: Obstruction theory 18D50: Operads

Information

Type
Research Article
Information
Compositio Mathematica , Volume 147 , Issue 2 , March 2011 , pp. 633 - 648
Copyright
Copyright © Foundation Compositio Mathematica 2010

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