By L. F. McAuley

**Read or Download Algebraic and Geometrical Methods in Topology: Conference on Topological Methods in Algebraic Topology SUNY Binghamton, October 3–7, 1973 PDF**

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**Additional resources for Algebraic and Geometrical Methods in Topology: Conference on Topological Methods in Algebraic Topology SUNY Binghamton, October 3–7, 1973**

**Example text**

Is said to be quasi-regular for a s ~ Research supported in part by NSF grant GP-38024. K consisting of a 45 product of spheres and sphere bundles Bn(P) ing In [10], Mimura and Toda mod p cohomology isomorphisms. and a map f:K--~X induc- characterize the quasi-regular primes for the compact, simply connected, simple Lie groups. Naturally one wonders to what extent quasi- regularity depends only on the H - structure. The main result of this paper is: Theorem i. Let X be a simply connected finite H - space with the largest entry in its type.

Moreover this principal refinement will be such that the fibre at each stage is a space K(A,n), where is P-local abelian. A = ri. 6, for some i, and it is easy to see [ 3 ] that FiB is n P-local if B is P-local. Given g: X ~ Z, the obstructions to the existence and uniqueness of a counterimage to lie in the groups H*(f;A) g under f* will thus and, as in the corresponding argument in the 1-connected case (note that we have trivial coefficients here, too), these groups will vanish if f induces P-localization in homology.

When either is missing from the type of For example, in the case of 4p- 3 1 < m < q p=5 When and The q = 3 m = 2 we both 7 is missing, so (b) is satisfied. which is the result in [i0]. Together, Theorems i and 2 contain the sufficient conditions for quasiregularity proved by Mimura and Toda. By means of results of [ii], the above Theorems can be formulated more geometrically. If p is a is quasi-regular for mod lence. We denote by p isomorphism the~ X X(p) X the localization of ( X as in Theorem 1 or 2) and f(p):K(p) --~X(p) at p .