Sanki, B and Gadgil, S (2019) Graphs of systoles on hyperbolic surfaces. In: Journal of Topology and Analysis, 11 (1). pp. 1-20.
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Abstract
Given a hyperbolic surface, the set of all closed geodesics whose length is minimal 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 main result is that this condition is also sufficient. 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, for instance, to the classical result that there are only two minimal non-planar graphs).
| Item Type: | Journal Article |
|---|---|
| Publication: | Journal of Topology and Analysis |
| Publisher: | World Scientific Publishing Co. Pte Ltd |
| Additional Information: | The copyright for this article belongs to the Author(s). |
| Keywords: | fat-graph; geodesic; Hyperbolic surface; length spectrum; systole |
| Department/Centre: | Division of Physical & Mathematical Sciences > Mathematics |
| Date Deposited: | 28 Oct 2022 05:48 |
| Last Modified: | 28 Oct 2022 05:48 |
| URI: | https://eprints.iisc.ac.in/id/eprint/77718 |
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