{"paper":{"title":"The topology of the space of symplectic balls in rational 4-manifolds","license":"","headline":"","cross_cats":["math.DG"],"primary_cat":"math.SG","authors_text":"Francois Lalonde, Martin Pinsonnault","submitted_at":"2002-07-11T18:02:23Z","abstract_excerpt":"We study in this paper the rational homotopy type of the space of symplectic embeddings of the standard ball $B^4(c) \\subset \\R^4$ into 4-dimensional rational symplectic manifolds. We compute the rational homotopy groups of that space when the 4-manifold has the form $M_{\\lambda}= (S^2 \\times S^2, \\mu \\omega_0 \\oplus \\omega_0)$ where $\\omega_0$ is the area form on the sphere with total area 1 and $\\mu$ belongs to the interval $[1,2]$. We show that, when $\\mu$ is 1, this space retracts to the space of symplectic frames, for any value of $c$. However, for any given $1 < \\mu < 2$, the rational ho"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0207096","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"}