# Existence of quasigeodesic Anosov flows in hyperbolic 3-manifolds

Dia | 2024-03-01 15:30:00-03:00 |

Hora | 2024-03-01 15:30:00-03:00 |

Lugar | Salón 703 (Rojo) FING |

### Existence of quasigeodesic Anosov flows in hyperbolic 3-manifolds

#### Sergio Fenley (Florida State University)

A quasigeodesic in a manifold is a curve so that when lifted to the universal cover is uniformly efficient up to a bounded multiplicative and added error in measuring length. A flow is quasigeodesic if all flow lines are quasigeodesics. We prove that an Anosov flow in a closed hyperbolic manifold is quasigeodesic if and only if it is not R-covered. Here R-covered means that the stable 2-dim foliation of the flow, lifts to a foliation in the universal cover whose leaf space is homeomorphic to the real numbers. There are many examples of quasigeodesic Anosov flows in closed hyperbolic 3-manifolds. There are consequences for the continuous extension property of Anosov foliations, and the existence of group invariant Peano curves associated with Anosov flows.