Classifying space for O(n)

In mathematics, the classifying space for O(n) may be constructed as the Grassmannian of n-planes in an infinite-dimensional real Hilbert space.

It is analogous to the classifying space for U(n).

This topology-related article is a stub. You can help Wikipedia by expanding it.v · Categories: Topology stubs Algebraic topology Wikimedia Foundation. 2010. Игры ⚽ Поможем написать реферат Aneirin Hughes Seaside Treats Look at other dictionaries: Classifying space for U(n) — In mathematics, the classifying space for the unitary group U(n) is a space B(U(n)) together with a universal bundle E(U(n)) such that any hermitian bundle on a paracompact space X is the pull back of E by a map X → B unique up to homotopy. This… …   Wikipedia 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 for which all its homotopy groups are trivial) by a free action of G. It… …   Wikipedia Space science — is an all encompassing term that describes all of the various science fields that are concerned with the study of the Universe, generally also meaning excluding the Earth and outside of the Earth s atmosphere . Originally, all of these fields… …   Wikipedia Space group — In mathematics and geometry, a space group is a symmetry group, usually for three dimensions, that divides space into discrete repeatable domains. In three dimensions, there are 219 unique types, or counted as 230 if chiral copies are considered… …   Wikipedia Complex projective space — The Riemann sphere, the one dimensional complex projective space, i.e. the complex projective line. In mathematics, complex projective space is the projective space with respect to the field of complex numbers. By analogy, whereas the points of a …   Wikipedia Real projective space — In mathematics, real projective space, or RP n is the projective space of lines in R n +1. It is a compact, smooth manifold of dimension n , and a special case of a Grassmannian.ConstructionAs with all projective spaces, RP n is formed by taking… …   Wikipedia Covering space — A covering map satisfies the local triviality condition. Intuitively, such maps locally project a stack of pancakes above an open region, U, onto U. In mathematics, more specifically algebraic topology, a covering map is a continuous surjective… …   Wikipedia Acyclic space — In mathematics, an acyclic space is a topological space X in which cycles are always boundaries, in the sense of homology theory. This implies that the integral homology groups in all dimensions of X are isomorphic to the corresponding homology… …   Wikipedia Moduli space — In algebraic geometry, a moduli space is a geometric space (usually a scheme or an algebraic stack) whose points represent algebro geometric objects of some fixed kind, or isomorphism classes of such objects. Such spaces frequently arise as… …   Wikipedia Symmetric space — In differential geometry, representation theory and harmonic analysis, a symmetric space is a smooth manifold whose group of symmetries contains an inversion symmetry about every point. There are two ways to make this precise. In Riemannian… …   Wikipedia 18+ © Academic, 2000-2024 Contact us: Technical Support, Advertising Dictionaries export, created on PHP, Joomla, Drupal, WordPress, MODx. Mark and share Search through all dictionaries Translate… Search Internet Share the article and excerpts Direct link … Do a right-click on the link above and select “Copy Link”