Algebraic & Geometric Topology

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

Nitu Kitchloo and W Stephen Wilson

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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
Received: 12 November 2014
Revised: 2 February 2015
Accepted: 2 February 2015
First available in Project Euclid: 16 November 2017

Permanent link to this document
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

Subjects
Primary: 55R45: Homology and homotopy of $B$O and $B$U; Bott periodicity 55N15: $K$-theory [See also 19Lxx] {For algebraic $K$-theory, see 18F25, 19- XX}
Secondary: 55N20: Generalized (extraordinary) homology and cohomology theories 55N22: Bordism and cobordism theories, formal group laws [See also 14L05, 19L41, 57R75, 57R77, 57R85, 57R90]

Keywords
Morava $K$—theory BO characteristic classes

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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