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^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

25 Citations (Scopus)

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]).

Original language	English
Pages (from-to)	611-629
Number of pages	19
Journal	Advances in Mathematics
Volume	272
DOIs	https://doi.org/10.1016/j.aim.2014.12.020
Publication status	Published - 6 Feb 2015
Externally published	Yes

Keywords

53C20
57R60
Eells-Kuiper projective plane
Exotic sphere
Isoparametric function
Morse-Bott function
SC-structure

Access to Document

10.1016/j.aim.2014.12.020

Cite this

@article{7b9a851aab644202a31a7c14cee1bddd,

title = "Isoparametric functions on exotic spheres",

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 B{\'e}rard-Bergery [2] (see also pp. 234-235 of [3]).",

keywords = "53C20, 57R60, Eells-Kuiper projective plane, Exotic sphere, Isoparametric function, Morse-Bott function, SC-structure",

author = "Chao Qian and Zizhou Tang",

note = "Publisher Copyright: {\textcopyright} 2014 Elsevier Inc.",

year = "2015",

month = feb,

day = "6",

doi = "10.1016/j.aim.2014.12.020",

language = "English",

volume = "272",

pages = "611--629",

journal = "Advances in Mathematics",

issn = "0001-8708",

publisher = "Academic Press Inc.",

}

TY - JOUR

T1 - Isoparametric functions on exotic spheres

AU - Qian, Chao

AU - Tang, Zizhou

PY - 2015/2/6

Y1 - 2015/2/6

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]).

KW - 53C20

KW - 57R60

KW - Eells-Kuiper projective plane

KW - Exotic sphere

KW - Isoparametric function

KW - Morse-Bott function

KW - SC-structure

UR - http://www.scopus.com/inward/record.url?scp=84920913829&partnerID=8YFLogxK

U2 - 10.1016/j.aim.2014.12.020

DO - 10.1016/j.aim.2014.12.020

M3 - Article

AN - SCOPUS:84920913829

SN - 0001-8708

VL - 272

SP - 611

EP - 629

JO - Advances in Mathematics

JF - Advances in Mathematics

ER -

Isoparametric functions on exotic spheres

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this