Let G be a discrete group and BG its classifying space. The author establishes some group properties which are invariants of the stable homotopy type of BG and proves that the following theorems are equivalent: Theorem A (Gorenstein and Walter). Let G be a finite group with a dihedral Sylow...
Priddy, “The complete stable splitting for the classifying space of a finite group” to appear in Topology. J.P. May, “Stable maps between classifying spaces”, Contemporary Math. 37, 1985. Mitchell, S., Priddy, S. (1984) Symmetric product spectra and splittings of classifying spaces. ...
Let G be a finite group and p a prime number. A homology decomposition of BG, the classifying space of G, is a map hocolimF→BG which is a mod p homology isomorphism. Here F is a functor from D, a small category, to the category of topological spaces such that for each object d...
We callEG→BGthe universal bundle,EGthe total space,BGthe classifying space. The explicit construction can be found in the bookCohomology of Finite Groups,Chapter II. Remark: In fact,A completely arbitrary topological groupGcan serve as the group of an n-universal bundle,n≤∞.Cf.Milnor's ...
For any group G there exists a classifying space BG, well defined up to homotopy. Classifying spaces are of central interest to geometers and topologists for the set of isomorphism classes of principal G-bundles over a space X is in one-to-one correspondence with the set of homotopy ...
The 1+1 G-cobordism category, with G a finite group, is important in the construction of G-topological field theories which are completely determined by a G-Frobenius algebra. We give a description of the classifying space of this category generalizing the work of Ulrike Tillmann. Moreover, ...
It fact the set of Fλ with λ4 = 1 is a threefold in the moduli space of finite algebras with a fixed basis, see [38] for construction of this space. Non-canonically graded algebras. We now classify forms F such that all polynomials f with leading form F lie in G· F. As in ...
摘要: We classify up to homotopy the self-maps of the classifying space of any non-affine Kac-Moody group of rank two. (C) 2003 Elsevier Science (USA). All rights reserved.关键词: Maps between classifying spaces of Kac¿Moody groups, Artículo ...
We prove that ZxB_{com}U is a loop space and define a notion of commutative K-theory for bundles over a finite complex X which is isomorphic to [X,ZxB_{com}U]. We compute the rational cohomology of B_{com}G for G equal to any of the classical groups U(n), SU(n) and Sp(n...
Let G be a finite group or a compact connected Lie group and let BG be its classifying space. Let ℒ BG ≔ map( S 1 , BG ) be the free loop space of BG , i.e. the space of continuous maps from the circle S 1 to BG . The purpose of this pap