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 | |
| 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
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Qian, C., & Tang, Z. (2015). Isoparametric functions on exotic spheres. Advances in Mathematics, 272, 611-629. https://doi.org/10.1016/j.aim.2014.12.020