We prove a slice theorem around closed leaves in a singular Riemannian foliation, and we use it to study the C∞-algebra of smooth basic functions, generalizing to the inhomogeneous setting a number of results by G. Schwarz. In particular, in the infinitesimal case we show that this algebra is generated by a finite number of polynomials.
A slice theorem for singular riemannian foliations, with applications
Radeschi M.
2019-01-01
Abstract
We prove a slice theorem around closed leaves in a singular Riemannian foliation, and we use it to study the C∞-algebra of smooth basic functions, generalizing to the inhomogeneous setting a number of results by G. Schwarz. In particular, in the infinitesimal case we show that this algebra is generated by a finite number of polynomials.
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