Universal homotopy associative, homotopy commutative H-spaces and the EHP spectral sequence

Details Universal homotopy associative, homotopy commutative H-spaces and the EHP spectral sequence Universal homotopy associative, homotopy commutative H-spaces and the EHP spectral sequence

2006-01-14

arxiv.org/abs/math/0601355v1

Mathematics

Algebraic Topology

29 pages

Scientific paper

10.1017/S0305004106009182

Assume that all spaces and maps are localised at a fixed prime $p$. We study the possibility of generating a universal space $U(X)$ from a space $X$ which is universal in the category of homotopy associative, homotopy commutative H-spaces in the sense that any map f:X->Y to a homotopy associative, homotopy commutative H-space extends to a uniquely determined H-map F: U(X)->Y. Developing a method for recognising certain universal spaces, we show the existence of the universal space F_2(n) of a certain three-cell complex L. Using this specific example, we derive some consequences for the calculation of the unstable homotopy groups of spheres, namely, we obtain a formula for the d_1-differential of the EHP-spectral sequence valid in a certain range.

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