Laplacian algebras, manifold submetries and the Inverse Invariant Theory Problem

Ricardo A. E. Mendes, Marco Radeschi

备注：: 33 pages. Final version. To appear in GAFA

英文摘要：

Manifold submetries of the round sphere are a class of partitions of the round sphere that generalizes both singular Riemannian foliations, and the orbit decompositions by the orthogonal representations of compact groups. We exhibit a one-to-one correspondence between such manifold submetries and maximal Laplacian algebras, thus solving the Inverse Invariant Theory problem for this class of partitions. Moreover, a solution to the analogous problem is provided for two smaller classes, namely orthogonal representations of finite groups, and transnormal systems with closed leaves.

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