Anick's fibration and the odd primary homotopy exponent of spheres

Details Anick's fibration and the odd primary homotopy exponent of spheres Anick's fibration and the odd primary homotopy exponent of spheres

2008-03-21

arxiv.org/abs/0803.3205v1

Mathematics

Algebraic Topology

25 pages

Scientific paper

For primes p>=3, Cohen, Moore, and Neisendorfer showed that the exponent of the p-torsion in the homotopy groups of S^2n+1 is p^n. This was obtained as a consequence of a thorough analysis of the homotopy theory of Moore spaces. Anick further developed this for p>=5 by constructing a homotopy fibration S^2n-1 --> T^2n+1(p^r) --> Loop S^2n+1 whose connecting map is degree p^r on the bottom cell. A much simpler construction of such a fibration for p>=3 was given by Gray and the author using new methods. In this paper the new methods are used to start over, first constructing Anick's fibration for p>=3, and then using it to obtain the exponent result for spheres.

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