Homotopical uniqueness of classifying spaces
نویسندگان
چکیده
منابع مشابه
Homotopical Uniqueness of Classifying Spaces
If G is a connected compact Lie group, then for almost all prime numbers p the mod p cohomology ring of the classifying space BG is a finitely generated polynomial algebra. In 1961, N. Steenrod [24] asked in general for a determination of all spaces X such that H∗(X,Fp) is a finitely generated polynomial algebra (i.e., such that X has a polynomial cohomology ring); at that time, the only exampl...
متن کاملHOMOTOPICAL EXCISION, AND HUREWICZ THEOREMS, FOR n-CUBES OF SPACES
where e is induced by the ‘excision’ inclusion. That e is an isomorphism in a range of dimensions is shown by the classical Blakers-Massey triad connectivity theorem: if A, B, and A∩B are connected, {A,B} is an open cover of X and (A, A ∩ B) is p-connected, (B, A ∩ B) is q-connected, then the triad (X; A,B) is (p + q)-connected. (See, for example, [11, p. 211].) Further, if p, q > 2 and π1(A∩B)...
متن کاملMaps between Classifying Spaces
In 1976, Adams & Mahmud 3] published the rst systematic study of the problem of determining the homological properties of maps between classifying spaces of compact connected Lie groups. This was continued in later work by one or both authors: Adams 2] extended some of the results to the case of non-connected Lie groups by using complex K-theory; while Adams & Mahmud 4] identiied further restri...
متن کاملAlgebraic Cobordism of Classifying Spaces
We define algebraic cobordism of classifying spaces, Ω∗(BG) and G-equivariant algebraic cobordism Ω∗G(−) for a linear algebraic group G. We prove some properties of the coniveau filtration on algebraic cobordism, denoted F (Ω(−)), which are required for the definition to work. We show that G-equivariant cobordism satisfies the localization exact sequence. We calculate Ω(BG) for algebraic groups...
متن کاملRational equivalences between classifying spaces
The paper contains a homotopy classification of rational equivalences between classifying spaces of compact connected Lie groups with an application to genus sets of such spaces. Mathematics Subject Classification (1991): 55R35, 55P10, 55P60, 55S37
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Topology
سال: 1992
ISSN: 0040-9383
DOI: 10.1016/0040-9383(92)90062-m