Event
Anja Randecker, University of Toronto
Wednesday, December 6, 2017 15:00to16:00
Burnside Hall
Room 920, 805 rue Sherbrooke Ouest, Montreal, QC, H3A 0B9, CA
Topology of infinite translation surfaces
Classical translation surfaces can be obtained from gluing finitely many polygons along parallel edges of the same length. In recent years, people have asked what happens when you glue infinitely instead of finitely many polygons. From that question the field of infinite translation surfaces has evolved. It turns out that the behaviour of infinite translation surfaces is in many regards very different and more diverse than in the classical case. This includes that for classical translation surfaces, we have a Gau脽鈥揃onnet formula which relates the cone angle of the singularities (coming from the corners of the polygons) to the genus of the surface. For infinite translation surfaces, we might observe so-called wild singularities for which the notion of cone angle is not applicable any more. In this talk, I will explain that there is still a relation between the geometry and the topology of infinite translation surfaces in the spirit of a Gau脽-Bonnet formula. In fact, under some weak conditions, the existence of a wild singularity implies infinite genus.
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