Isoparametric functions on exotic spheres |
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Authors: | Chao Qian Zizhou Tang |
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Affiliation: | 1. School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, PR China;2. School of Mathematical Sciences, Laboratory of Mathematics and Complex Systems, Beijing Normal University, Beijing 100875, PR China |
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Abstract: | This paper extends widely the work in [11]. Existence and non-existence results of isoparametric functions on exotic spheres and Eells–Kuiper projective planes are established. In particular, every homotopy n -sphere (n>4) carries an isoparametric function (with certain metric) with 2 points as the focal set, in strong contrast to the classification of cohomogeneity one actions on homotopy spheres [26] (only exotic Kervaire spheres admit cohomogeneity one actions besides the standard spheres). As an application, we improve a beautiful result of Bérard-Bergery [2] (see also pp. 234–235 of [3]). |
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Keywords: | 53C20 57R60 |
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