1-Manifolds Galore!

Laurence Siebenmann
University of Paris-SUD
Professor of Mathematics

“I will present a combinatorial classifcation, up to homeomorphism, of all simply connected, separable, non-Hausdorff, 1-dimensional  manifolds (possibly with boundary), each having only finitely many singular points. These often occur as the leaf space of a codimension 1 foliation of a metrizable manifold of dimension 2 or more. For example, the leaf space of a plane foliation defined by polynomials has finitely many singular points. For all codimension 1 topological foliations of R ⁿ, n ≥ 3, with all leaves homeomorphic to R ^n-1, it is a reasonable conjecture that the leaf space alone classifies the foliation topologically; see Carlos Palmeira, Annals 1978, for a partial proof”.