{"paper":{"title":"On homological rigidity and flexibility of exact Lagrangian endocobordisms","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":"2013-10-06T11:56:34Z","abstract_excerpt":"We show that an exact Lagrangian cobordism $L\\subset \\mathbb R \\times P \\times \\mathbb R$ from a Legendrian submanifold $\\Lambda\\subset P\\times \\mathbb R$ to itself satisfies $H_i(L;\\mathbb F)=H_i(\\Lambda;\\mathbb F)$ for any field $\\mathbb F$ in the case when $\\Lambda$ admits a spin exact Lagrangian filling and the concatenation of any spin exact Lagrangian filling of $\\Lambda$ and $L$ is also spin. The main tool used is Seidel's isomorphism in wrapped Floer homology. In contrast to that, for loose Legendrian submanifolds of $\\mathbb{C}^n \\times \\mathbb R$, we construct examples of such cobord"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.1577","kind":"arxiv","version":5},"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"}