Chennai Mathematical Institute


11:50 am, Seminar Hall
Graphs of systoles on hyperbolic surfaces

Bidyut Sanki
Institute of Mathematical Sciences, Chennai.


In this talk, we study the configuration of systoles (minimum length geodesics) on closed hyperbolic surfaces. The set of all systoles forms a graph on the surface, in fact a so-called fat graph, which we call the systolic graph. We study which fat graphs are systolic graphs for some surface, we call these admissible. There is a natural necessary condition on such graphs, which we call combinatorial admissibility. Our first result characterises admissibility.

It follows that a sub-graph of an admissible graph is admissible. Our second major result is that there are infinitely many minimal non-admissible fat graphs (in contrast, to the classical result that there are only two minimal non-planar graphs).