20 April 2016, 16:00 - 17:00, in HG00.310
Ricardo Mendes (Universität Münster)
"Invariant Theory" of infinitesimal singular Riemannian foliations
Singular Riemannian foliations can be seen as natural generalizations
of the decomposition of Riemannian manifolds into orbits of isometric
group actions. In this context we prove a Slice Theorem which, as in
the homogeneous case, describes the local structure around any closed
leaf in terms of a natural foliation on the normal space to the leaf
at a point. Such "slice foliations" are examples of "infinitesimal
foliations", which are a natural generalization of Representations.
Moreover, infinitesimal foliations are "algebraic", by a recent result
of A.Lytchak and M. Radeschi.
In this talk I will describe, in addition to the Slice Theorem, some of our results on the "Invariant Theory" of infinitesimal foliations. Namely, we give a description of the smooth functions that are constant on the leaves (generalizing Schwarz's Theorem), and find a connection between infinitesimal foliations and Jordan algebras. The latter allows one to classify "degree 2" infinitesimal foliations, and generalize the familiar notions of isotypical components, decomposition into irreducible subspaces, and (real/complex/quaternionic) "type" from Representation Theory.