Hauptseminar Geometrie

Translation surfaces arise in many different contexts, for example in the theory of abelian differentials on Riemann surfaces. A classical method to construct them is by gluing finitely many polygons in the plane along parallel edges of the same length. For these surfaces, there exists a translation atlas on the whole surface except of the former vertices of the polygons which are called singularities. If we start from this point of view and consider connected surfaces with a translation atlas, we obtain the notion of infinite translation surfaces. In contrast to the classical case, infinite translation surfaces don't have to be compact, for example. Therefore, this definition is clearly a generalization of the classical translation surfaces but it is not obvious in which terms the surfaces are infinite. In this talk, I will discuss which geometric properties (area, type of singularities, ...) or topological properties (genus, space of ends, ...) can indicate if a surface with a translation atlas is a finite or an infinite translation surface.

Dienstag, den 3. Februar 2015 um 13:30 Uhr, in INF288, HS5 Dienstag, den 3. Februar 2015 at 13:30, in INF288, HS5