Adam Moreno, UCLA

Title: Locating the Boundary of Leaf Spaces with Pre-Sections

Abstract: We develop further the notion of a "pre-section" for
a singular Riemannian foliation as a proper submanifold retaining all
the tranverse geometric information of the foliation. These pre-sections
are a form of reduction similar to that what one sees for polar isometric
group actions. We show that if a positively curved Riemannian manifold,
equipped with a singular Riemannian foliation, contains a nontrivial
pre-section, then the resulting leaf space has boundary. In particular,
we recover as a corollary a known result about polar foliations while also
generalizing in the special case of foliations induced by isometric group
actions. This is joint work with Diego Corro.