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Proceedings of the American Mathematical Society

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

 

 

Some relations between semigroups of polyhedra


Author: Ilan Kozma
Journal: Proc. Amer. Math. Soc. 39 (1973), 388-394
MSC: Primary 55D10
DOI: https://doi.org/10.1090/S0002-9939-1973-0315702-9
MathSciNet review: 0315702
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Abstract: All spaces are CW-complexes of finite type. The notation ``='' means homotopy equivalence. The following theorems are proved:

(1) If $ X \vee A = Y \vee A$ then there exists $ T$ such that $ \Omega X \times T = \Omega Y \times T$,

(2) $ X \times A = Y \times A$ implies that there is a $ T$ such that $ \Sigma X \vee T = \Sigma Y \vee T$.

A partial converse is also proved. As a corollary we get that if $ X \vee A = Y \vee A$ then $ {\pi _ \ast }(X) = {\pi _ \ast }(Y)$ and if $ X \times A = Y \times A$ then $ {h_ \ast }(X) = {h_ \ast }(Y)$ for many homology theories.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1973-0315702-9
Keywords: Noncancellation, suspension, one point union, loop spaces, product, homotopy groups, homology groups
Article copyright: © Copyright 1973 American Mathematical Society