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By L. F. McAuley

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

Example text

Smith Different approaches to [15] and Bousfield and Kan [2], [3]. We state the central fact on which our proofs are based. denote a product of odd dimensional spheres Bn(P). Consider the case of Theorem 1. can be found with 2m+l H*(X; Zp) & H*(K; Zp) Thus the mod p ! 4p-3 and S 2m+l and sphere bundles n ! P-I cohomology of X such that has the form E2 b'(M) where can be read off from as in Figure i. mod p is an Now the fact that <__6 p - 5 . E2 . Furthermore all the This implies that if one writes down the geometric realization of a minimal resolution of obtains essentially the M of the spectral sequence there are no non-trivial differentials in stems 6p -5 , K abstractly as algebras over the Steenrod algebra.

7 Let X Be a connected CW-complex. y if its Postnikov system admits a princzpal refinement. 33 We point out that the simple spaces are identified, by the correspondence implicit in this corollary, with those spaces whose Postnikov system is itself principal. 4. Localization of nilpotent complexes In this section we extend Theorems 2A and 2B from the category to the category N. To do so we need, of course, to have the notion of the localization of nilpotent groups. properties, H1 This notion, together with the relevant is to be found in[2,3], but we repeat the definition here for the reader's convenience.

1973) (to appear). 3. P. J. Hilton, Remarks on the localization of nilpotent groups, Comm. Pure and Applied Math. (1973) (to appear). 4. P. J. Hilton, G. Mislin and J. Roitberg, Homotoplcal localization, Proc. Lond. Math. Soc. 3, XXVI (1973), 693-706. 5. P. J. Hilton, G. Mislin and J. Roitberg, H-spaces of rank 2 and non-cancellation phenomena, Inv. Math. 16 (1972), 325-334. 6. P. J. Hilton and Joe Roitberg, On principal S3-bundles over sphere, Ann. of Math. 90 (1969), 91-107. 7. M. Mimura, G.

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