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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

On mapping cones of suspension elements of finite order in the homotopy groups of a wedge of spheres


Author: Imre Bokor
Journal: Proc. Amer. Math. Soc. 119 (1993), 955-961
MSC: Primary 55P15
MathSciNet review: 1152974
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Abstract: The genus of the mapping cone $ {C_f}$ of a map $ f:{S^{m - 1}} \to \bigvee{S^n}(m > n > 1)$ representing a suspension element of finite order in $ {\pi _{m - 1}}(\bigvee{S^n})$ is classified by a subgroup $ {G_f}$ of $ {\pi _{m - 1}}({S^n})$ depending only on the homotopy type of $ {C_f}$. The group $ {G_f}$ finds application in proving that the genus of $ {C_f}$ is trivial whenever $ {C_f}$ has sufficiently many $ n$-cells, the number being limited by the torsion subgroup of $ {\pi _{m - 1}}({S^n})$.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1993-1152974-8
PII: S 0002-9939(1993)1152974-8
Keywords: CW complex, genus, suspension
Article copyright: © Copyright 1993 American Mathematical Society