{"paper":{"title":"Concentrating Local Solutions of the Two-Spinor Seiberg-Witten Equations on 3-Manifolds","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math-ph","math.GT","math.MP"],"primary_cat":"math.DG","authors_text":"Gregory J. Parker","submitted_at":"2022-10-15T00:30:59Z","abstract_excerpt":"Given a compact 3-manifold $Y$ and a $\\mathbb Z_2$-harmonic spinor $(\\mathcal Z_0, A_0,\\Phi_0)$ with singular set $\\mathcal Z_0$, this article constructs a family of local solutions to the two-spinor Seiberg-Witten equations parameterized by $\\epsilon \\in (0,\\epsilon_0)$ on tubular neighborhoods of $\\mathcal Z_0$. These solutions concentrate in the sense that the $L^2$-norm of the curvature near $\\mathcal Z_0$ diverges as $\\epsilon\\to 0$, and after renormalization they converge locally to the original $\\mathbb Z_2$-harmonic spinor. In a sequel to this article, these model solutions are used in"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2210.08148","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2210.08148/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}