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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
The Morava $K$–theory of $BO(q)$ and $MO(q)$

Nitu Kitchloo and W Stephen Wilson

Algebraic & Geometric Topology 15 (2015) 3047–3056
Abstract

We give an easy proof that the Morava K–theories for BO(q) and MO(q) are in even degrees. Although this is a known result, it had followed from a difficult proof that BP(BO(q)) was Landweber flat. Landweber flatness follows from the even Morava K–theory. We go further and compute an explicit description of K(n)(BO(q)) and K(n)(MO(q)) and reconcile it with the purely algebraic construct from Landweber flatness.

Keywords
Morava $K$—theory, BO, characteristic classes
Mathematical Subject Classification 2010
Primary: 55R45, 55N15
Secondary: 55N20, 55N22
References
Publication
Received: 12 November 2014
Revised: 2 February 2015
Accepted: 2 February 2015
Published: 10 December 2015
Authors
Nitu Kitchloo
Department of Mathematics
Johns Hopkins University
Baltimore, MD 21218
USA
W Stephen Wilson
Department of Mathematics
Johns Hopkins University
Baltimore, MD 21218
USA