{"paper":{"title":"Local maxima of the systole function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Kasra Rafi, Maxime Fortier Bourque","submitted_at":"2018-07-22T21:04:03Z","abstract_excerpt":"We construct infinite families of closed hyperbolic surfaces that are local maxima for the systole function on their respective moduli spaces. The systole takes values along a linearly divergent sequence $(L_n)_{n\\geq 1}$ at these local maxima. The only surface corresponding to $L_1\\approx 3.057$ is the Bolza surface in genus $2$. For every genus $g\\geq 13$, we obtain either one or two local maxima in $\\mathcal{M}_g$ whose systoles have length $L_2\\approx 5.909$. For each $n\\geq 3$, there is an arithmetic sequence of genera $(g_k)_{k\\geq 1}$ such that the number of local maxima of the systole "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.08367","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}