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Singular Riemannian foliations, manifold submetries, and Laplacian algebras

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Ricardo Mendes
Universität zu Köln
Thu, 2019-01-24 16:30 - 17:30
MPIM Lecture Hall

(Joint work with M. Radeschi.) Singular Riemannian foliations of the
round sphere S^n are decompositions of S^n into smooth, equidistant
submanifolds. They generalize both the orbit decomposition under the
isometric action of a connected group, and isoparametric foliations.
By a result of Lytchak-Radeschi, such foliations are always algebraic,
in the sense that the algebra of polynomials that are constant on
leaves is finitely generated, and separates leaves. This establishes a
one-to-one correspondence between such foliations and *some* class of
algebras of polynomials. In this talk I will give a characterization
of the algebras that arise in this way, in the more general context of
manifold submetries.

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