JournalsjemsVol. 24, No. 2pp. 623–668

Local maxima of the systole function

  • Maxime Fortier Bourque

    University of Glasgow, UK
  • Kasra Rafi

    University of Toronto, Canada
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We construct a sequence of closed hyperbolic surfaces that are local maxima for the systole function in their respective moduli spaces. Their systole is arbitrarily large and the number of examples grows rapidly with the genus. More precisely, for every n3n\geq 3 there is some positive number LnL_n (growing roughly linearly in nn) such that the number of local maxima of the systole function in genus gg with systole equal to LnL_n grows super-exponentially in gg along an arithmetic sequence of step size nn. Many of these surfaces have no orientation-preserving isometries other than the identity and are the first examples of local maxima with this property.

Cite this article

Maxime Fortier Bourque, Kasra Rafi, Local maxima of the systole function. J. Eur. Math. Soc. 24 (2022), no. 2, pp. 623–668

DOI 10.4171/JEMS/1113