A fiberwise analogue of the Borsuk-Ulam theorem for sphere bundles over a 2-cell complex II |
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Authors: | Ryuichi Tanaka |
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Affiliation: | Department of Liberal Arts, Faculty of Science and Technology, Tokyo University of Science, Noda, Chiba, 278-8510 Japan |
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Abstract: | We describe a finite complex B as I-trivial if there does not exist a Z2-map from Si−1 to S(α) for any vector bundle α over B and any integer i with i>dimα. We prove that the m-fold suspension of projective plane FP2 is I-trivial if and only if m≠0,2,4 for F=C, m≠0,4 for F=H. In the case where F is the Cayley algebra, the m-fold suspension is shown to be I-trivial for every m>0. |
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Keywords: | primary, 55P91 secondary, 55R25 |
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