Abelian properties of Anick spaces

Brayton Gray

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arXiv · 1208.3733

Abelian properties of Anick spaces

Brayton Gray

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Abstract

The Anick spaces play a key role in an unstable filtration of the stable homotopy of V(0) to produce secondary EHP sequences. This work establishes that the Anick spaces are homotopy associative and homotopy commutative H-spaces, and that they have a universal mapping property for maps into a homotopy commutative and homotopy associative H-space with a (necessary) condition on the growth of the p torsion. This is utilized to establish an unstable composition theory. The techniques involve generalized Whitehead products based on co-H spaces, calculations in a congruence category that lies between the unstable category and the stable category, and a controlled version of the extension theorem for principal fibrations.

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Brayton Gray. 2012-08-18. Abelian properties of Anick spaces. https://arxiv.org/abs/1208.3733

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