group cohomology, nonabelian group cohomology, Lie group cohomology
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A localization of complex bordism that maps to ordinary Morava K-theory.
For instance (Kriz-Sati 04, p. 41/385, Buhné, def. 4.2.4).
The orientation of integral Morava K-theory is discussed in (Sati-Kriz 04, Buhné 11). It is essentially given by the vanishing of the seventh integral Stiefel-Whitney class $W_7$.
Notice that this is in analogy to how orientation in complex K-theory is given by the vanishing third integral Stiefel-Whitney class $W_3$ (spin^c-structure).
Precisely:
Let $X$ be a connected closed manifold of dimension 10 with spin structure. This is generalized oriented in second integral Morava K-theory $\tilde K(2)$ (for $p = 2$) precisely if its seventh integral Stiefel-Whitney class vanishes, $W_7(X) = 0$.
This is (Buhné 11, prop. 8.1.13), following (Sati-Kriz 04).
Let $X$ be a connected closed manifold of dimension 10 with spin structure. This is generalized oriented in second Johnson-Wilson cohomology theory (Morava E-theory) $E(2)$ (for $p = 2$) precisely if its seventh integral Stiefel-Whitney class vanishes, $W_7(X) = 0$.
This is (Buhné 11, cor. 8.1.14), following (Sati-Kriz 04).
See at Diaconescu-Moore-Witten anomaly.
Math. Phys. 8 (2004), no. 2, 345–394 (arXiv:hep-th/0404013)
Last revised on June 17, 2013 at 21:28:09. See the history of this page for a list of all contributions to it.