In mathematics, the classifying space for the unitary group U(n) is a space BU(n) together with a universal bundle EU(n) such that any hermitian bundle...

Classifying space for O(n), BO(n) Classifying space for U(n), BU(n) Classifying space for SO(n) Classifying space for SU(n) Classifying stack Borel's...

{\displaystyle \operatorname {SO} } . Classifying space for O(n) Classifying space for U(n) Classifying space for SU(n) Milnor, John; Stasheff, James (1974)...

\operatorname {O} } . Classifying space for U(n) Classifying space for SO(n) Classifying space for SU(n) Milnor, John; Stasheff, James (1974). Characteristic...

classifying space BSU ⁡ ( n ) {\displaystyle \operatorname {BSU} (n)} for the special unitary group SU ⁡ ( n ) {\displaystyle \operatorname {SU} (n)}...

polynomial is identically zero. The classifying space for U(n) is described in the article Classifying space for U(n). Special unitary group Projective...

group U(n) for n big enough. If we find EU(n) then we can take EG to be EU(n). The construction of EU(n) is given in classifying space for U(n). The following...

classical notion of classifying space of a discrete group; see below for details. Let C be a small category. There is a 0-simplex of N(C) for each object of...

classifying spaces in K-theory, notably the classifying space for U(n). In the homotopy theory of schemes, the Grassmannian plays a similar role for algebraic...

unitary group U in Bott's sense has a classifying space BU for complex vector bundles (see Classifying space for U(n)). A deeper application coming from...

equivalences K ( Z , 1 ) ≃ U ( 1 ) ≃ B Z {\displaystyle K(\mathbb {Z} ,1)\simeq U(1)\simeq B\mathbb {Z} } for the classifying space B Z {\displaystyle B\mathbb...

space, just as the projective orthogonal group is the isometry group of real projective space. In terms of matrices, elements of U(n) are complex n×n...

\ldots \end{aligned}}} For the theory associated to the infinite unitary group, U, the space BU is the classifying space for stable complex vector bundles...

arbitrary positive scalar) the problem of classifying topological invariants reduces to the problem of classifying all possible inequivalent choices of Γ...

over the classifying space B U ( n ) {\displaystyle BU(n)} of the unitary group U ( n ) {\displaystyle U(n)} . The natural inclusion from U ( n ) {\displaystyle...

{\displaystyle n\to \infty } . It is BU(1), the classifying space of U(1), the circle group, in the sense of homotopy theory, and so classifies complex line...

classifier is the one nearest neighbour classifier that assigns a point x to the class of its closest neighbour in the feature space, that is C n 1 n...

configuration space of the plane UConf n ⁡ ( R 2 ) {\displaystyle \operatorname {UConf} _{n}(\mathbf {R} ^{2})} is a classifying space for the Artin braid...

Volodin space X {\displaystyle X} of a ring R is a subspace of the classifying space B G L ( R ) {\displaystyle BGL(R)} given by X = ⋃ n , σ B ( U n ( R )...

free actions. Those spaces can serve as the universal principal bundles, and the quotients for the actions as the classifying spaces B G {\displaystyle...

Sierpiński. The Sierpiński space has important relations to the theory of computation and semantics, because it is the classifying space for open sets in the Scott...

→ N {\displaystyle \operatorname {Homeo} (F)\to M_{p}\to N} . The theory of classifying spaces gives us an induced push-forward fibration M p → N → B...

topological space X , {\displaystyle X,} named for Leopold Vietoris, is generated by the following basis: for every n {\displaystyle n} -tuple U 1 , … , U n {\displaystyle...

the classifying space B G {\displaystyle BG} . Homogeneous space Heap (mathematics) Serge Lang and John Tate (1958). "Principal Homogeneous Space Over...

Strickland, Neil P. (2009). "The category of CGWH spaces" (PDF). McCord, M. C. (1969), "Classifying spaces and infinite symmetric products", Transactions...

Sign Language, particular classifier handshapes represent a noun's orientation in space. There are similarities between classifier systems and noun classes...

especially popular for classifying short texts. It has the benefit of explicitly modelling the absence of terms. Note that a naive Bayes classifier with a Bernoulli...

impossible to have a fine moduli space. However, it is often possible to consider a modified moduli problem of classifying the original objects together...

combinations than grid search. The final model, which is used for testing and for classifying new data, is then trained on the whole training set using the...

defined as the union of all finite H P n {\displaystyle \mathbb {HP} ^{n}} 's under inclusion, is the classifying space BS3. The homotopy groups of H P ∞ {\displaystyle...