In
mathematics, the
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 ...
for the
orthogonal group O(''n'') may be constructed as the
Grassmannian
In mathematics, the Grassmannian is a space that parameterizes all -dimensional linear subspaces of the -dimensional vector space . For example, the Grassmannian is the space of lines through the origin in , so it is the same as the projective ...
of ''n''-planes in an infinite-dimensional real space
.
It is analogous to the
classifying space for U(''n'').
{{topology-stub
Algebraic topology