Filling surfaces with very few systoles
Abstract
In the paper we describe hyperbolic surfaces filled by their systoles, where the total number of systoles is in O(g \,g), that is equivalent to the lower bound of Anderson, Parlier and Pittet APP. Various papers SSFB20Sanki IM Mathieu have investigated the same question, and the best previously known upper bounds where in o(g \,g). Surprizingly the present approach is, in our opinion, much simpler than the methods of earlier papers.
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