Borel's theorem

Not to be confused with Borel's theorem on power series.

In topology, a branch of mathematics, Borel's theorem, due to Armand Borel (1953), says the cohomology ring of a classifying space or a classifying stack is a polynomial ring.

See also

• Atiyah–Bott formula

References

• Borel, Armand (1953). "Sur la cohomologie des éspaces fibrés principaux et des éspaces homogènes de groupes de Lie compacts". Annals of Mathematics. 57 (1): 115–207. doi:10.2307/1969728. JSTOR 1969728. MR 0051508.
• Behrend, Kai A. (2003). "Derived l-adic categories for algebraic stacks". Memoirs of the American Mathematical Society. 163 (774). doi:10.1090/memo/0774. MR 1963494.