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...
Stable splittings of classifying spaces of amalgams of finite groups The Bianchi group Γ -1 is defined to be PSL 2 (O -1 ) where O -1 is the ring of integers in (i). The author proves that BΓ -1 , the classifying space of Γ -1 , stably splits at the prime 3 as B 3 ...
One way to understand the mod p homotopy theory of classifying spaces of finite groups is to compute their BZ/p-cellularization. In the easiest cases this is a classifying space of a finite group (always a finite p-group). If not, we show that it has infinitely many non-trivial homotopy...
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. ...
Theorem 1. Let G be a compact connected simple Lie group and let p be an odd prime which divides the order of the Weyl group. Suppose X is a p-complete space such that Zrl(X) is finite, that H*(X; Fp) is of finite type, and that the component of the space of based maps ...
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 ...
Let G be a locally compact topological group. We investigate the type of the classifying space of G for the family of compact subgroups. We give criteria for this space to have a d-dimensional G-CW -model, a finite G-CW -model or a G-CW -model of finite type. Essentially we reduce...
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1. A classification of the stable type of BG. Let G be a finite group. We denote BG a classifying space of G, which has a contractible universal principal G bundle EG. With G. Carlsson's solution of the Segal conjecture it has become possible to determine the complete p-local stable ...
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, ...