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Invariant Theory for singular Riemannian foliations

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Marco Radeschi
Universität Münster
Thu, 2016-06-30 16:30 - 17:30
MPIM Lecture Hall
Singular Riemannian foliations are foliation on Riemannian
manifolds whose leaves are equidistant. Singular Riemannian foliations 
on Euclidean spaces (called infinitesimal foliations), are of special
importance since they provide the local models for general singular
Riemannian foliation around a point, and generalize orthogonal
representations up to orbit equivalence. A recent result with A.Lytchak
shows that infinitesimal foliations are given by the preimages of some
polynomial map. In this talk, we show how this new algebraic structure
leads to new algebraic objects, describing the structure of the foliation.
In particular, we show how the space of quadratic basic polynomials (i.e.
polynomials that are constant on the leaves of the foliation) produces a
Jordan algebra which encodes information about the structure of invariant
subspaces of the foliation.
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