The Morava K–theory of BO(q) and MO(q)

Kitchloo, Nitu; Wilson, W Stephen

doi:10.2140/agt.2015.15.3049

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The Morava $K$–theory of $BO(q)$ and $MO(q)$

Nitu Kitchloo and W Stephen Wilson

Algebraic & Geometric Topology 15 (2015) 3047–3056

DOI: 10.2140/agt.2015.15.3049

Abstract

We give an easy proof that the Morava $K$ –theories for $B O (q)$ and $M O (q)$ are in even degrees. Although this is a known result, it had followed from a difficult proof that ${B P}^{*} (B O (q))$ was Landweber flat. Landweber flatness follows from the even Morava $K$ –theory. We go further and compute an explicit description of $K {(n)}_{*} (B O (q))$ and $K {(n)}_{*} (M O (q))$ 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

Volume 15, issue 5 (2015)