{"paper":{"title":"Estimating the number of Reeb chords using a linear representation of the characteristic algebra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SG","authors_text":"Georgios Dimitroglou Rizell, Roman Golovko","submitted_at":"2014-09-22T18:51:29Z","abstract_excerpt":"Given a chord-generic horizontally displaceable Legendrian submanifold $\\Lambda\\subset P\\times \\mathbb R$ with the property that its characteristic algebra admits a finite-dimensional matrix representation, we prove an Arnold-type lower bound for the number of Reeb chords on $\\Lambda$. This result is a generalization of the results of Ekholm-Etnyre-Sullivan and Ekholm-Etnyre-Sabloff which hold for Legendrian submanifolds whose Chekanov-Eliashberg algebras admit augmentations. We also provide examples of Legendrian submanifolds $\\Lambda$ of $\\mathbb C^{n}\\times \\mathbb R$, $n \\ge 1$, whose char"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.6278","kind":"arxiv","version":3},"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"}