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Register a new userLaplacian algebras, manifold submetries and the Inverse Invariant Theory Problem
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Ricardo Augusto Emmanuel Mendes
Publication date
2019
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and research's language is
English
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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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