Atiyah–Bott formula

For other uses, see Atiyah–Bott fixed-point theorem.

In algebraic geometry, the Atiyah–Bott formula says^[1] the cohomology ring

${\displaystyle \operatorname {H} ^{*}(\operatorname {Bun} _{G}(X),\mathbb {Q} _{l})}$

of the moduli stack of principal bundles is a free graded-commutative algebra on certain homogeneous generators. The original work of Michael Atiyah and Raoul Bott concerned the integral cohomology ring of ${\displaystyle \operatorname {Bun} _{G}(X)}$.

See also

• Borel's theorem, which says that the cohomology ring of a classifying stack is a polynomial ring.