Isoparametric functions on exotic spheres
Differential Geometry
2014-12-30 v2 Geometric Topology
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 -sphere () 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} ).
Cite
@article{arxiv.1303.6028,
title = {Isoparametric functions on exotic spheres},
author = {Chao Qian and Zizhou Tang},
journal= {arXiv preprint arXiv:1303.6028},
year = {2014}
}
Comments
18 pages. References are updated, and some typos are corrected due to the referees. To appear in Adv. Math