On the rationalization of the circle
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- by Carles Casacuberta PDF
- Proc. Amer. Math. Soc. 118 (1993), 995-1000 Request permission
Abstract:
We give an example showing that, for a nilpotent group $G$ and a set of primes $P$, the $P$-localization homomorphism $l:G \to {G_P}$ need not induce an isomorphism in cohomology with arbitrary (twisted) ${{\mathbf {Z}}_P}$-module coefficients. From this fact we infer that, in the pointed homotopy category of connected CW-complexes, the inclusion of the subcategory of spaces whose higher homotopy groups are ${{\mathbf {Z}}_P}$-modules and whose fundamental group is uniquely ${P’}$-radicable does not admit a left adjoint.References
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Additional Information
- © Copyright 1993 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 118 (1993), 995-1000
- MSC: Primary 55P60; Secondary 20J05
- DOI: https://doi.org/10.1090/S0002-9939-1993-1176479-3
- MathSciNet review: 1176479