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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

Self-maps of loop spaces. I


Authors: H. E. A. Campbell, F. P. Peterson and P. S. Selick
Journal: Trans. Amer. Math. Soc. 293 (1986), 1-39
MSC: Primary 55P47; Secondary 55P10, 55P35, 55P45
MathSciNet review: 814910
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Abstract: In this paper we study self-maps of $ {\Omega ^k}{S^{m + 1}}$ and show that, except for the cases $ m = 1,\,3,\,7$, or $ p$ and $ m$, if $ f$ induces an isomorphism on $ {H_{m + 1 - k}}({\Omega ^k}{S^{m + 1}};\,Z/pZ)$ with $ k < m$, then $ {f_{(p)}}$ is a homotopy equivalence.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1986-0814910-1
PII: S 0002-9947(1986)0814910-1
Article copyright: © Copyright 1986 American Mathematical Society