Leaf topology of minimal foliations on 3-manifolds

Speaker: Carlos Meniño, UFF.

Date: 11 oct 2019, 15h30m.

Place: Room 407, Bloco H, Campus Gragoatá, UFF.

Abstract: We show that every oriented and noncompact surface is homeomorphic to a leaf of a minimal hyperbolic foliation of a closed 3-manifold. The example is a suspension of a suitable circle group action over the bitorus. Moreover, every prescribed countable family of noncompact oriented surfaces can be simultaneusly realized as leaves of the same minimal hyperbolic foliation. The interest of this example relies in the fact that there were no examples of minimal hyperbolic foliatons with leaves with leaves with finitely and infinitely generated groups coexisting in the same foliation (and in the first case, only foliations with leaves homeomorphic to planes and cylinders were described!). Our example cannot be smoothed to transverse regularity C2, this suggests possible obstructions on the leaf topology of minimal hyperbolic foliations in that regularity. This is a joint work with P. Gusmão (UFF).