Atiyah–Bott formula

From HandWiki
Revision as of 00:14, 7 February 2024 by JTerm (talk | contribs) (linkage)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Short description: On the cohomology ring of the moduli stack of principal bundles

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

[math]\displaystyle{ \operatorname{H}^*(\operatorname{Bun}_G(X), \mathbb{Q}_l) }[/math]

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 [math]\displaystyle{ \operatorname{Bun}_G(X) }[/math].

See also

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

Notes

References