- Online only
- On sale!
DIGITAL BOOKSHOP OF THE USC
Un teorema de Hedlund para fibrados foliados sobre superficies hiperb´olicas
- Autor/a
- Carballido Costas, Alvaro
In this work we will attempt to generalize the classical Hedlund’s theorem about theminimality of the horocycle flow to the foliated case. This problem has been formulated by M. Martínez and A. Verjovsky. We will focus on foliated manifolds by hyperbolic surfaces obtained by the suspension of a representation:
ρ : ΓT Difeor+(S1)
of a surface group Γ on the group of orientation-preserving Cr diffeomorphisms of S1,0 ≤ r ≤ ∞.
For non-faithful representations, we give an elementary proof of the minimality of the horocycle flow. Nevertheless, to prove the minimality of the horocycle flow for faithful representations, we have to use a general result due to S. Matsumoto that assumes the minimality of the B+-action on the unit tangent bundle of the foliation. In the particular case of faithful representations of surface groups on PSL(2,R) we have the following dichotomy:
If the representation is discrete, then the horocycle flow is not minimal, but there is aunique minimal set that coincides with the unique minimal set of the B+-action.
If the representation is not discrete, we prove the minimality of the B+-action which, using Matsumoto’s theorem, gives us the minimality of the horocycle flow.
Data sheet
- Edition
- 1
- Publication place
- Santiago de Compostela
- Publication Year
- 2020
- Serie
- 143a Publicaciones del Departamento de Geometría y Topología
- Availability
- Si
In this work we will attempt to generalize the classical Hedlund’s theorem about theminimality of the horocycle flow to the foliated case. This problem has been formulated by M. Martínez and A. Verjovsky. We will focus on foliated manifolds by hyperbolic surfaces obtained by the suspension of a representation:
ρ : ΓT Difeor+(S1)
of a surface group Γ on the group of orientation-preserving Cr diffeomorphisms of S1,0 ≤ r ≤ ∞.
For non-faithful representations, we give an elementary proof of the minimality of the horocycle flow. Nevertheless, to prove the minimality of the horocycle flow for faithful representations, we have to use a general result due to S. Matsumoto that assumes the minimality of the B+-action on