{"paper":{"title":"The homotopy type of the space of symplectic balls in rational ruled 4-manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SG","authors_text":"Francois Lalonde, Martin Pinsonnault, Silvia Anjos","submitted_at":"2008-07-07T15:13:04Z","abstract_excerpt":"Let M:=(M^{4},\\om) be a 4-dimensional rational ruled symplectic manifold and denote by w_{M} its Gromov width. Let Emb_{\\omega}(B^{4}(c),M) be the space of symplectic embeddings of the standard ball B^4(c) \\subset \\R^4 of radius r and of capacity c:= \\pi r^2 into (M,\\om). By the work of Lalonde and Pinsonnault, we know that there exists a critical capacity \\ccrit \\in (0,w_{M}] such that, for all c\\in(0,\\ccrit), the embedding space Emb_{\\omega}(B^{4}(c),M) is homotopy equivalent to the space of symplectic frames \\SFr(M). We also know that the homotopy type of Emb_{\\omega}(B^{4}(c),M) changes wh"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0807.1031","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"}