{"paper":{"title":"Resonance for loop homology of spheres","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.DG","authors_text":"Hans-Bert Rademacher, Nancy Hingston","submitted_at":"2011-05-04T10:10:37Z","abstract_excerpt":"A Riemannian or Finsler metric on a compact manifold M gives rise to a length function on the free loop space \\Lambda M, whose critical points are the closed geodesics in the given metric. If X is a homology class on \\Lambda M, the minimax critical level cr(X) is a critical value. Let M be a sphere of dimension >2, and fix a metric g and a coefficient field G. We prove that the limit as deg(X) goes to infinity of cr(X)/deg(X) exists. We call this limit the \"global mean frequency\" of M. As a consequence we derive resonance statements for closed geodesics on spheres; in particular either all hom"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.0783","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"}