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arXiv · 1303.6028

Isoparametric functions on exotic spheres

Chao Qian·Zizhou Tang
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Abstract

This paper extends widely the work in \cite{GT13}. 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 \cite{St96} ( only exotic Kervaire spheres admit cohomogeneity one actions besides the standard spheres ). As an application, we improve a beautiful result of B\'{e}rard-Bergery \cite{BB77} ( see also pp.234-235 of \cite{Be78} ).

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Chao Qian, Zizhou Tang. 2013-03-25. Isoparametric functions on exotic spheres. https://arxiv.org/abs/1303.6028

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