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arXiv · 1706.02917

Cancellation and homotopy rigidity of classical functors

Ruizhi Huang·Jie Wu
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Abstract

We first show that simply connected co-$H$-spaces and connected $H$-spaces can be uniquely decomposed into prime factors in the homotopy category of pointed $p$-local spaces of finite type, which is used to develop a $p$-local version of Gray's correspondence between homotopy types of prime co-$H$-spaces and homotopy types of prime $H$-spaces, and the split fibration which connects them as well. Further, we use the unique decomposition theorem to study the homotopy rigidity problem for classic functors. Among others, we prove that $ΣΩ$ and $Ω$ are homotopy rigid on simply connected $p$-local co-$H$-spaces of finite type, and $ΩΣ$ and $Σ$ are homotopy rigid on connected $p$-local $H$-spaces of finite type.

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BibTeXRIS

Ruizhi Huang, Jie Wu. 2019-05-10. Cancellation and homotopy rigidity of classical functors. https://doi.org/10.1112/jlms.12167

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