A minimal foliation on a 3-manifold with a non-trivial geometrically finite leaf

Carlos Meniño Cotón (Río de Janeiro)

Xoves 14 de xuño de 2018 ás 16 horas na aula 7.


We show how to construct a (hyperbolic) minimal foliation on a compact 3-manifold with a leaf homeomorphic to a punctured torus. A surface is said to be of finite geometry if its fundamental group is finitely generated. As far as we know this is the first explicit example of minimal foliation on a closed 3-manifold with leaves of finite geometry other than planes and cylinders. Our example is transversely continuous although, almost surely, it could be improved to class C1; some conjectures in 1-dimensional dynamics and results on hyperbolic foliations seem to imply that this is the highest regularity in which this kind of examples can happen.

This is a joint work (in progress) with Paulo Gusmão (UFF).

© Carlos Meniño Cotón.