Loop spaces of finite complexes at large primes
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- by C. A. McGibbon and C. W. Wilkerson
- Proc. Amer. Math. Soc. 96 (1986), 698-702
- DOI: https://doi.org/10.1090/S0002-9939-1986-0826505-X
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Abstract:
Let $X$ be a finite, simply connected CW complex with only a finite number of nonzero rational homotopy groups. Localized away from a certain finite set of primes, the loop space of $X$ is shown to be homotopy equivalent to a product of spheres and loop spaces of spheres. Applications to the homotopy groups of $X$ and the homological properties of $\Omega X$ are given.References
- David J. Anick, A loop space whose homology has torsion of all orders, Pacific J. Math. 123 (1986), no.Β 2, 257β262. MR 840843
- F. R. Cohen, J. C. Moore, and J. A. Neisendorfer, Torsion in homotopy groups, Ann. of Math. (2) 109 (1979), no.Β 1, 121β168. MR 519355, DOI 10.2307/1971269
- Stephen Halperin, Finiteness in the minimal models of Sullivan, Trans. Amer. Math. Soc. 230 (1977), 173β199. MR 461508, DOI 10.1090/S0002-9947-1977-0461508-8
- I. M. James, On the suspension sequence, Ann. of Math. (2) 65 (1957), 74β107. MR 83124, DOI 10.2307/1969666
- Hirosi Toda, On the double suspension $E^2$, J. Inst. Polytech. Osaka City Univ. Ser. A 7 (1956), 103β145. MR 92968
Bibliographic Information
- © Copyright 1986 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 96 (1986), 698-702
- MSC: Primary 55Q52; Secondary 55P35
- DOI: https://doi.org/10.1090/S0002-9939-1986-0826505-X
- MathSciNet review: 826505