{"paper":{"title":"Mazur manifolds and symplectic structures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Heegaard Floer cobordism maps obstruct symplectic structures on specific Akbulut-Kirby Mazur manifolds bounded by Brieskorn spheres.","cross_cats":["math.SG"],"primary_cat":"math.GT","authors_text":"Alberto Cavallo","submitted_at":"2026-05-14T17:14:03Z","abstract_excerpt":"We use the Heegaard Floer homology cobordism maps to obstruct the existence of a symplectic structure on the Akbulut-Kirby Mazur manifolds whose boundary is a Brieskorn sphere $Y$ among $\\Sigma(2,3,13),$ $\\Sigma(2,5,7)$ and $\\Sigma(3,4,5)$. Furthermore, we describe how our results imply the existence of exotic pairs of simply connected 4-manifolds, with definite intersection form, whose boundary is $Y$."},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We use the Heegaard Floer homology cobordism maps to obstruct the existence of a symplectic structure on the Akbulut-Kirby Mazur manifolds whose boundary is a Brieskorn sphere Y among Σ(2,3,13), Σ(2,5,7) and Σ(3,4,5).","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The Heegaard Floer cobordism maps for the specific 2-handles and the chosen Brieskorn spheres detect the absence of a symplectic structure without additional assumptions on the filling or on the contact structure induced on the boundary.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Mazur manifolds with boundaries Σ(2,3,13), Σ(2,5,7), and Σ(3,4,5) admit no symplectic structure, producing exotic pairs of simply connected 4-manifolds with definite intersection forms.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Heegaard Floer cobordism maps obstruct symplectic structures on specific Akbulut-Kirby Mazur manifolds bounded by Brieskorn spheres.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"1ff4f48145381a066d55c8e4da7a85b4c0c6da12c268ba6e444e5aed38bcb79d"},"source":{"id":"2605.15095","kind":"arxiv","version":1},"verdict":{"id":"11aada87-749b-4738-a157-c7e25e4e3cdf","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-15T02:55:29.613335Z","strongest_claim":"We use the Heegaard Floer homology cobordism maps to obstruct the existence of a symplectic structure on the Akbulut-Kirby Mazur manifolds whose boundary is a Brieskorn sphere Y among Σ(2,3,13), Σ(2,5,7) and Σ(3,4,5).","one_line_summary":"Mazur manifolds with boundaries Σ(2,3,13), Σ(2,5,7), and Σ(3,4,5) admit no symplectic structure, producing exotic pairs of simply connected 4-manifolds with definite intersection forms.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The Heegaard Floer cobordism maps for the specific 2-handles and the chosen Brieskorn spheres detect the absence of a symplectic structure without additional assumptions on the filling or on the contact structure induced on the boundary.","pith_extraction_headline":"Heegaard Floer cobordism maps obstruct symplectic structures on specific Akbulut-Kirby Mazur manifolds bounded by Brieskorn spheres."},"references":{"count":24,"sample":[{"doi":"","year":2020,"title":"S. Akbulut,Cork twists and automorphisms of3-manifolds, J. Gökova Geom. Topol. GGT.,14(2020), pp. 1–13","work_id":"44b56a2e-59e7-469e-85e0-8de4df860400","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2004,"title":"S. Akbulut and S. Durusoy,An involution acting nontrivially on Heegaard-Floer homology, Geometry and topology of manifolds. Papers from the conference held at McMaster University, Hamilton, ON, Canada","work_id":"2f60600e-9030-4cbc-a16a-ec8724823f64","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2011,"title":"S. Akbulut and Ç. Karakurt,Action of the Cork twist on Floer homology, Proceedings of the 18th Gökova geometry-topology conference, Gökova, Turkey, May 30–June 4, 2011","work_id":"aeb8b9ee-ad3f-40f4-a924-62071398f329","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1979,"title":"S. Akbulut and R. Kirby,Mazur manifolds, Michigan Math. J.,26(1979), no. 3, pp. 259–284","work_id":"751e0541-95cb-48af-83f2-ab4955837f5c","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2018,"title":"S. Akbulut and K. Larson,Brieskorn spheres bounding rational balls, Proc. Amer. Math. Soc.,146(2018), no. 4, pp. 1817–1824","work_id":"a8dca7d2-be2f-4d66-aa14-f5629f8c0d31","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":24,"snapshot_sha256":"488bf19296e356e565a7475a8338caad6fe81b398504a399125eb698ab2a58d6","internal_anchors":2},"formal_canon":{"evidence_count":2,"snapshot_sha256":"d7a3c11faeeaad6767cc78a7be4d8c91e19d2bd9960bca3b0b36bfca2047c873"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}