2008/10/31 by Vigleik Angeltveit · 1 citation
Mathematics · #Advanced Operator Algebra Research #Algebraic structures and combinatorial models #Homotopy #Homotopy and Cohomology in Algebraic Topology #Moduli space #Ring (chemistry) #Sequence (biology) #Set (abstract data type) #Spectral sequence #Uniqueness #math.AT #msc:55N20
paper · pdf · doi:10.1112/s0010437x10005026
16 pages. Minor modifications, to appear in Compositio Mathematica.
arxiv created 2010/05/06 · openalex publication_date 2010/09/27 · arxiv updated 2014/01/14 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
Abstract 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 connective S -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.