Isoparametric functions on exotic spheres

By Chao Qian, Zizhou Tang. 2013

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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 Berard-Bergery [2] (see also pp. 234–235 of [3] ).

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/ebfc664181392db9b9324133f33768ba702de9b1