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• Tags:
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• Links:
  • FGL
  • Landweber exactness

complex oriented cohomology theory

• A condition on a generalized cohomolology theories involving the Thom class:

Think of this as a factorization of the counit

https://q.uiver.app/?q=WzAsMyxbMCwwLCJcXFNTIl0sWzIsMCwiWCBcXGRhIFxcU2lnbWFee1xcaW5mdHktMn1cXENQXntcXGluZnR5fSJdLFs0LDAsIkUiXSxbMSwyLCJ4XkUiXSxbMCwyLCJcXGV0YV9FIiwyLHsiY3VydmUiOjV9XSxbMCwxLCJcXGV0YV9YIl1d

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