Session S23 - Group actions in Differential Geometry

Wednesday, July 14, 11:00 ~ 11:30 UTC-3

Manifold submetries, with applications to Invariant Theory

Marco Radeschi

University of Notre Dame, United States   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

Given an orthogonal representation of a Lie group G on a Euclidean vector space V, Invariant Theory studies the algebra of G-invariant polynomials on V. This setting can be generalized by replacing the orbits of the representation with a foliation by the fibers of a manifold submetry from the unit sphere S(V), and consider the algebra of polynomials that are constant along these fibers (effectively producing an Invariant Theory, but without groups). In this talk we will exhibit a surprisingly strong relation between the geometric information coming from the submetry and the algebraic information coming from the corresponding algebra, with several applications to classical Invariant Theory.

Joint work with Ricardo Mendes.

View abstract PDF