On decompositions in homotopy theory

Gray, Brayton

doi:10.1090/S0002-9947-05-03964-4

On decompositions in homotopy theory
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Trans. Amer. Math. Soc. 358 (2006), 3305-3328 Request permission

Abstract:

We first describe Krull-Schmidt theorems decomposing $H$ spaces and simply-connected co-$H$ spaces into atomic factors in the category of pointed nilpotent $p$-complete spaces of finite type. We use this to construct a 1-1 correspondence between homotopy types of atomic $H$ spaces and homotopy types of atomic co-$H$ spaces, and construct a split fibration which connects them and illuminates the decomposition. Various properties of these constructions are analyzed.

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