Isoparametric functions on exotic spheres

Chao Qian; Zizhou Tang

doi:10.1016/j.aim.2014.12.020

Isoparametric functions on exotic spheres

Chao Qian
, Zizhou Tang^*

^*此作品的通讯作者

University of Chinese Academy of Sciences
Beijing Normal University

科研成果: 期刊稿件 › 文章 › 同行评审

32 引用（Scopus）

摘要

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]).

源语言	英语
页（从-至）	611-629
页数	19
期刊	Advances in Mathematics
卷	272
DOI	https://doi.org/10.1016/j.aim.2014.12.020
出版状态	已出版 - 6 2月 2015
已对外发布	是

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AU - Qian, Chao

AU - Tang, Zizhou

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N2 - 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]).

AB - 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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KW - Eells-Kuiper projective plane

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KW - Morse-Bott function

KW - SC-structure

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VL - 272

SP - 611

EP - 629

JO - Advances in Mathematics

JF - Advances in Mathematics

ER -

Isoparametric functions on exotic spheres

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