{"paper":{"title":"Floer cohomology of immersed Lagrangian spheres in smoothings of $A_N$ surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SG","authors_text":"Garrett Alston","submitted_at":"2013-11-11T01:50:51Z","abstract_excerpt":"We calculate the self-Floer cohomology with Z/2 coefficients of some immersed Lagrangian spheres in the affine symplectic submanifolds of C^3 that are smoothings of A_N surfaces. The immersed spheres are exact and graded. Moreover, they satisfy a positivity assumption that allows us to calculate the Floer cohomology as follows: Given auxiliary data a Morse function on S^2 and a time-dependent almost complex structure, the Floer cochain complex is the Morse complex plus two generators for each self-intersection point of the Lagrangian sphere. The Floer differential is defined by counting combin"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.2327","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"}