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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

A strong homotopy axiom for Alexander cohomology


Author: Kermit Sigmon
Journal: Proc. Amer. Math. Soc. 31 (1972), 271-275
DOI: https://doi.org/10.1090/S0002-9939-1972-0287533-9
MathSciNet review: 0287533
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Abstract: It is shown that the following form of the homotopy axiom holds for Alexander-Čech cohomology. Suppose that $ X$ and $ Y$ are any spaces, that $ T$ is a compact, connected space, and that $ G$ is an abelian group which either admits the structure of a compact topological group or is the additive group of a finite-dimensional vector space. Then for any continuous function $ F:X \times T \to Y$, one has $ F_r^\ast = F_s^\ast:{H^\ast}(Y;G) \to {H^\ast}(X;G)$ for all $ r,s \in T$, where $ {F_t}:X \to Y$ is defined by $ {F_t}(x) = F(x,t)$.


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DOI: https://doi.org/10.1090/S0002-9939-1972-0287533-9
Article copyright: © Copyright 1972 American Mathematical Society