{"paper":{"title":"Spectral numbers and manifolds with boundary","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SG","authors_text":"Darko Milinkovi\\'c, Jelena Kati\\'c, Jovana Nikoli\\'c","submitted_at":"2019-01-23T16:49:27Z","abstract_excerpt":"We consider a smooth submanifold $N$ with a smooth boundary in an ambient closed manifold $M$ and assign a spectral invariant $c(\\alpha,H)$ to every singular homological class $\\alpha\\in H_*(N)$ and a Hamiltonian $H$ defined on the cotangent bundle $T^*M$. We also derive certain properties of spectral numbers, for example we prove that spectral invariants $c_\\pm(H,N)$ associated to the whole Floer homology $HF_*(H,N:M)$ of the submanifold $N$, are limits of the decreasing nested family of open sets."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.07995","kind":"arxiv","version":1},"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"}