11:50 am, Seminar Hall
Graphs of systoles on hyperbolic surfaces
Bidyut Sanki
Institute of Mathematical Sciences, Chennai.
19-09-18

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Abstract

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).