Webderstand the topology of the classifying space BHof a homeomor-phism group His to consider a map f: B → BHdefined on a space with understood topology and, for example, examine the induced map on the cohomology. In the present paper we mostly investigate the homomorphism H∗(BH)→ H∗(BG)for the natural action of a
Classifying space - Encyclopedia of Mathematics
Webthe cohomology of the classifying space of H. It follows that in the equivariant theory there is much more freedom of movement. Another important feature of equivariant cohomology is that there is a theory of equivariant Chern classes. A G-linearization of a vector WebNov 26, 2016 · Group (co)homology and classyfing spaces. I would like to ask where I can find in the literature the proof of the following fact: the group cohomology of the group G … gunnebo fire extinguisher
The relation between group cohomology and the cohomology …
WebCOHOMOLOGY OF CLASSIFYING SPACES AND HERMITIAN REPRESENTATIONS GEORGE LUSZTIG Abstract. It is shown that a large part of the cohomology of the classifying space of a Lie group satisfying certain hypotheses can be obtained by a dif- ference construction from hermitian representations of that Lie group. WebApr 10, 2024 · However, we know that even for the ordinary classifying space BG for infinite groups G, BG could be different for the different choices of topology for G, e.g., discrete or continuous topologies. 27 27. J. D. Stasheff, “ Continuous cohomology of groups and classifying spaces,” Bull. Am. Math. Soc. 84(4), 513– 530 (1978). As explained later, this means that classifying spaces represent a set-valued functor on the homotopy category of topological spaces. The term classifying space can also be used for spaces that represent a set-valued functor on the category of topological spaces, such as Sierpiński space. See more 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 … See more A more formal statement takes into account that G may be a topological group (not simply a discrete group), and that group actions of G are taken to be continuous; in the absence of continuous actions the classifying space concept can be dealt with, in … See more • Classifying space for O(n), BO(n) • Classifying space for U(n), BU(n) • Classifying stack • Borel's theorem • Equivariant cohomology See more An example of a classifying space for the infinite cyclic group G is the circle as X. When G is a discrete group, another way to specify the condition on X is that the universal cover Y of X is contractible. In that case the projection map See more 1. The circle S is a classifying space for the infinite cyclic group $${\displaystyle \mathbb {Z} .}$$ The total space is 2. The n-torus See more This still leaves the question of doing effective calculations with BG; for example, the theory of characteristic classes is … See more 1. ^ Stasheff, James D. (1971), "H-spaces and classifying spaces: foundations and recent developments", Algebraic topology (Proc. Sympos. Pure Math., Vol. XXII, Univ. Wisconsin, Madison, Wis., 1970), American Mathematical Society, pp. 247–272 Theorem 2, See more bowser dealership