nLab EO(n)

Idea

A real form of Morava E-theory.

Properties

Orientation

The orientation in $EO(2)$-cohomology of a manifold with spin structure ($w_1 = 0$ and $w_2 = 0$) is essentially obstructed by the 4th Stiefel-Whitney class $w_4$ (Kriz-Sati 04, section 5.2).

References

The construction and general properties are discussed in

• Po Hu, Igor Kriz, Real-oriented homotopy theory and an analogue of the Adams-Novikov spectral sequence, Topology 40 (2001) (pdf)

The orientation in $EO(2)$-theory is discussed in section 5.2 of

• Igor Kriz, Hisham Sati, M-theory, type IIA superstrings, and elliptic cohomology, Adv. Theor.

  Math. Phys. 8 (2004), no. 2, 345–394 (arXiv:hep-th/0404013)