Speaker: David Miyamoto (MPIM)
Title: Leaf spaces of Killing foliations
Abstract: A Riemannian foliation is a foliation for which any two leaves are locally equidistant. By the Reeb stability theorem, every leaf space of a Riemannian foliation with compact leaves is an orbifold. We prove that, under mild completeness assumptions, the leaf space of a Killing Riemannian foliation - which includes Riemannian foliations of simply connected manifolds, and those induced by connected groups acting isometrically on compact Riemannian manifolds - is a diffeological quasifold: it is locally diffeomorphic to quotients of Cartesian space by countable group acting affinely. Furthermore, we show that the holonomy groupoid of a Killing foliation is, locally, Morita equivalent to the action groupoids of the aforementioned actions. This is joint work with Yi Lin.
