{"paper":{"title":"Quadratic enhancements of surfaces: two vanishing results","license":"","headline":"","cross_cats":["math.AT"],"primary_cat":"math.GT","authors_text":"Laurence R. Taylor","submitted_at":"2008-02-01T19:53:36Z","abstract_excerpt":"This note records two results which were inexplicably omitted from our paper on Pin structures on low dimensional manifolds, [KT]. Kirby chose not to be listed as a coauthor.\n  A Pin^- structure on a surface F induces a quadratic enhancement of the mod 2 intersection form, q: H_1(F;Z/2Z) -> Z/4Z\n  Theorem 1.1 says that q vanishes on the kernel of the map in homology to a bounding 3-manifold. This is used by Kreck and Puppe (arXiv:0707.1599 [math.AT]) who refer for a proof to an email of the author to Kreck. A more polished and public proof seems desirable.\n  In [KT], section 6, a Pin^- structu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0802.0111","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"}