5 papers
Non-linear proper Fredholm maps and the stable homotopy groups of spheres
Thomas O. Rot, Lauran Toussaint
We classify non-linear proper Fredholm maps between Hilbert spaces, up to proper homotopy, in terms of the stable homotopy groups of spheres. We show that there is a surjective map…
An elementary proof of Novikov's theorem
Samuel Ranz, Lauran Toussaint
Novikov's theorem states that, given a taut (codimension-one) foliation on a closed 3-manifold M, the fundamental group of any leaf injects into the fundamental group of M. We use…
Wrinkling h-principles for integral submanifolds of jet spaces
Álvaro del Pino, Lauran Toussaint
Y. Eliashberg and N. Mishachev introduced the notion of wrinkled embedding to show that any tangential homotopy can be approximated by a homotopy of topological embeddings with mil…
Existence of conformal symplectic foliations on closed manifolds
Fabio Gironella, Lauran Toussaint
We consider the existence of symplectic and conformal symplectic codimension-one foliations on closed manifolds of dimension at least 5. Our main theorem, based on a recent result…
Examples of symplectic non-leaves
Fabio Gironella, Lauran Toussaint
This paper deals with the following question: which manifolds can be realized as leaves of codimension-1 symplectic foliations on closed manifolds? We first observe that leaves of…