In
topology
In mathematics, topology (from the Greek words , and ) is concerned with the properties of a geometric object that are preserved under continuous deformations, such as stretching, twisting, crumpling, and bending; that is, without closing ho ...
, a branch of
mathematics, Borel's theorem, due to , says the
cohomology ring In mathematics, specifically algebraic topology, the cohomology ring of a topological space ''X'' is a ring formed from the cohomology groups of ''X'' together with the cup product serving as the ring multiplication. Here 'cohomology' is usually u ...
of a
classifying space
In mathematics, specifically in homotopy theory, a classifying space ''BG'' of a topological group ''G'' is the quotient of a weakly contractible space ''EG'' (i.e. a topological space all of whose homotopy groups are trivial) by a proper free ac ...
or a
classifying stack In algebraic geometry, a quotient stack is a stack that parametrizes equivariant objects. Geometrically, it generalizes a quotient of a scheme or a variety by a group: a quotient variety, say, would be a coarse approximation of a quotient stack.
Th ...
is a
polynomial ring
In mathematics, especially in the field of algebra, a polynomial ring or polynomial algebra is a ring (which is also a commutative algebra) formed from the set of polynomials in one or more indeterminates (traditionally also called variable ...
.
See also
*
Atiyah–Bott formula
In algebraic geometry, the Atiyah–Bott formula says the cohomology ring
:\operatorname^*(\operatorname_G(X), \mathbb_l)
of the moduli stack of principal bundles is a free graded-commutative algebra on certain homogeneous generators. The origi ...
Notes
References
*
*
{{topology-stub
Theorems in algebraic topology
Theorems in algebraic geometry