Some relations between semigroups of polyhedra
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- by Ilan Kozma PDF
- Proc. Amer. Math. Soc. 39 (1973), 388-394 Request permission
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.References
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Additional Information
- © Copyright 1973 American Mathematical Society
- 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