Abstract
In a previous paper, the authors gave the finest functorial decomposition of the loop suspension of a p-torsion suspension. The purpose of this paper is to generalize this theorem to the loop suspension of arbitrary p-local path connected spaces.
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References
Anick, D.: Homotopy exponents for spaces of category two. Lecture Notes in Mathematics 1370, 24–52 (1986)
Bousfield, A.K., Curtis, E.B.: A spectral sequence for the homotopy of nice spaces. Trans. AMS 151, 457–479 (1970)
Bousfield, Curtis, Kan, Quillen, Rector, Schlesinger: the mod-p lower central series and the Adams spectral sequence. Topology 5, 331–342 (1966)
Cohen, F.R.: Applications of loop spaces to some problems in topology. Lond. Math. Soc. Lect. Notes in Math 139, 11–20 (1985)
Cohen, F.: On combinatorial group theory in homotopy. Contemp. Math. 188, 57–63 (1995)
Cohen, Moore, Neisendorfer: The double suspension and exponents in the homotopy groups of spheres. Ann. of Math. 110, 121–168 (1979)
Curtis, Reiner: Methods of Representation Theory, Vol. I. Pure and Applied Mathematics, Wiley, 1981
Cohen, F.R., Wu, J.: A remark on the homotopy groups of Σnℝ P 2. Contemp. Math. 181, 65–81 (1995)
Curtis, E.B.: Simplicial homotopy theory. Advances in Math 6, 107–209 (1971)
Gordon James, Adalbert Kerber: The representation theory of the symmetric groups. Encyclopedia of Mathematics and its Applications 16, 1981
Kan, D.: On c.s.s. complexes. Amer. J. Math. 79, 449–476 (1957)
Kan, D.: A combinatorial definition of homotopy groups. Ann. of Math. 67, 288–312 (1958)
Milnor, J., Moore, J.: On the structure of Hopf Algebras. Ann. of Math. 81, 211–264 (1965)
Paul Selick, Jie Wu: On natural decompositions of loop suspensions and natural coalgebra decompositions of tensor algebras. Memoirs AMS 148, 2000
Paul Selick, Jie Wu: On Functorial Decompositions of Self-Smash Products. Manuscripta Math. 111, 435–457 (2003)
Paul Selick, Jie Wu: Some calculations of Lie(n)max for low n. Journal of Pure and Applied Algebra (to appear)
Wellington, R.J.: The unstable Adams spectral sequence for free iterated loop spaces. Memoirs AMS 258, 1982
Wu, J.: On combinatorial calculations for the James-Hopf maps. Topology 37, 1011–1023 (1998)
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The authors are grateful for support from
National Sciences Engineering Research Council of Canada and
National University of Singapore.
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Selick, P., Wu, J. The functor A min on p-local spaces. Math. Z. 253, 435–451 (2006). https://doi.org/10.1007/s00209-005-0909-3
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DOI: https://doi.org/10.1007/s00209-005-0909-3