Tetrahedra on deformed spheres and integral group cohomology.
This paper provides universal upper bounds for the exponent of the kernel and of the cokernel of the classical Boardman homomorphism b n: π n(X)→H n(H;ℤ), from the cohomotopy groups to the ordinary integral cohomology groups of a spectrum X, and of its various generalizations π n(X)→E n(X), F n(X)→(E∧F)n(X), F n(X)→H n(X;π 0 F) and F n(X)→H n+t(X;π t F) for other cohomology theories E *(−) and F *(−). These upper bounds do not depend on X and are given in terms of the exponents of the stable homotopy...
For the Brown-Peterson spectrum BP at the prime 3, denotes Hazewinkel’s second polynomial generator of . Let denote the Bousfield localization functor with respect to . A typical example of type one finite spectra is the mod 3 Moore spectrum M. In this paper, we determine the homotopy groups for the 8 skeleton X of BP.