Actividad formativa del máster y del doctorado en matemáticas.
Minicurso impartido como actividad formativa del máster y del doctorado en matemáticas.
Conferenciante: Maciej Czarnecki (University of Lodz)
Título: QUASI–GEODESIC FLOWS
Abstract: After Danny Calegari and Steven Frankel we describe a structure of quasi– geodesic flows on 3–dimensional hyperbolic manifolds. A flow in an action of the addirtive group R o on given manifold. We concentrate on closed 3–dimensional hyperbolic manifolds i.e. having locally isometric covering by the hyperbolic space H3. Such flow is quasi–geodesic if every flowline of the lifted flow is a quasi–geodesic in H3. Quasi–geodesic flows are probably the only reasonable metric objects which are foliations of hyperbolic 3–manifolds which do not carry neither geodesic foliation in any dimension (Zeghib) nor quasi–geodesic foliations of dimension 2 (Fenley). We start with foundations of hyperbolic manifolds, hyperbolic groups and their asympotic properties. Then we describe shortly notions for foliations and flows mentioning their type like (quasi)–isometric, (quasi)–geodesic, (pseudo)–Anosov etc. We take care of topology of the plane focusing on decompositions into continua. For such decompositions we construct a circular order in the set of their topological ends. Since after Calegari any quasi–geodesic flow on a hyperbolic 3 manifold has the Hausdorff flowspace (i.e. the plane) we are able to apply decompositions for a compactification the flowspace by ends of flowlines making it a closed disc. Finally, we study new results of Frankel on extension properties of quasi–geodesic flow. In particular we take a look for its proof of Calegari conjecture stating that such flows need to have closed orbits. At the end, we add some remarks about (quasi)–geodesic flows in non-compact case.
Fecha y lugar: 16, 17 y 18 de abril de 2018 de 9:00 a 11:00 horas en el seminario de la primera planta del IEMath-Gr