By L. F. McAuley

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

**Sample text**

If n = 2, then such a complex is merely a wedge of 2-spheres, X = VS 2 , where a runs through some index set, and we define Y = VM( ~p,2), where M(A,2) is the Moore space having H2M = A. There is then an evident 26 map f: X ~ Y f : X 0 ~ Y 0 satisfying satisfying (iii). Suppose now that we have constructed (iii) if dim X 0 S n, where n ~ 2, and let 0 dim X = n + i, X E H I . 4) VM(~p,n) where fo' fl satisfy if embeds Y j h :. 4) homotopy-commutes. 4) O by f: X + Y to a homotopy-commutative diagram and it is then easy to prove (using the exactness of the localization of abelian groups) that f: X ~ Y also satisfies satisfying (iii) if X (iii).

G. Kumpel, Mod p equivalences of J. Math. 23 (1972). rood p H - spaces, Qu~rt. 51 [7] M. Mahowald, On obstruction theory in orientable Trans. Amer. Math. Soc, II0 (1964), [8] W. S. Massey and F. P. Peterson, fibre bundles, 315-349. The cohomology structure of certain fibre spaces, Topology--4 (1965), 47-65. [9 ] and , On the rood 2 cohomology Structure of certain fibre spaces, Amer. Math. Soc. Memoirs [i0] 74 (1967). M. Mimura and H. Toda, Cohomology operations and the homotopy of compact Lie groups, Topology 9-- (1970), 317-336.

N We will prove Theorems 2A, 2B simultaneously. homomorphlsm is P-local and ~: A + B ~ We recall that a of abellan groups P-iocallzes if and only if B is a P-isomorphism [ 2 ] ; this latter conditions means that the kernel and cokernel of ~ torsion groups with torsion prime to belong to the Serre class P. C of abelian Thus to prove that (ii) ~ (iii) in Theorem 2B above it suffices to prove the following two propositions. *We write, as usual classes of maps from [Y,Z] Y to for Z. 1 Y ~ HI . 1 and o n l y i f P.