The -periodic homotopy groups of an unstable sphere at odd primes

Author:
Robert D. Thompson

Journal:
Trans. Amer. Math. Soc. **319** (1990), 535-559

MSC:
Primary 55Q40

DOI:
https://doi.org/10.1090/S0002-9947-1990-1010890-8

MathSciNet review:
1010890

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Abstract: The -periodic homotopy groups of a space are defined by considering the homotopy classes of maps of a Moore space into and then inverting the Adams self map. In this paper we compute the -periodic homotopy groups of an odd dimensional sphere, localized at an odd prime. This is done by showing that these groups are isomorphic to the stable -periodic homotopy groups of , the skeleton of the classifying space for the symmetric group . There is a map , where is a spectrum constructed from connective -theory, and the image in homotopy is studied.

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DOI:
https://doi.org/10.1090/S0002-9947-1990-1010890-8

Article copyright:
© Copyright 1990
American Mathematical Society