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complex oriented cohomology theory
- A condition on a generalized cohomolology theories involving the Thom class:
Think of this as a factorization of the counit
A ring spectrum \(E\) is complex orientable iff the Atiyah Hirzebruch spectral sequence collapses at \(E_2\): \begin{align*} E_{2}^{p, q}=H^{p}\left(\mathbb{C} P^{\infty} ; \pi_{q}(E)\right) \Longrightarrow E^{p+q}\left(\mathbb{C} P^{\infty}\right) \end{align*}
Motivations
