## Algebraic & Geometric Topology

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

#### 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.

#### Article information

Source
Algebr. Geom. Topol., Volume 15, Number 5 (2015), 3047-3056.

Dates
Revised: 2 February 2015
Accepted: 2 February 2015
First available in Project Euclid: 16 November 2017

https://projecteuclid.org/euclid.agt/1510841042

Digital Object Identifier
doi:10.2140/agt.2015.15.3049

Mathematical Reviews number (MathSciNet)
MR3426703

Zentralblatt MATH identifier
1329.55017

#### Citation

Kitchloo, Nitu; Wilson, W Stephen. The Morava $K$–theory of $BO(q)$ and $MO(q)$. Algebr. Geom. Topol. 15 (2015), no. 5, 3047--3056. doi:10.2140/agt.2015.15.3049. https://projecteuclid.org/euclid.agt/1510841042

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