{"paper":{"title":"Index theorem for Z/2-harmonic spinors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Ryosuke Takahashi","submitted_at":"2017-05-04T18:00:57Z","abstract_excerpt":"In my previous paper, I prove the existence of the Kuranishi structure for the moduli space $\\mathfrak{M}$ of zero loci of $\\mathbb{Z}/2$-harmonic spinors on a 3-manifold. So a nature question we can ask is to compute the virtual dimension for this moduli space $\\mathfrak{M}_{g_0}:=\\mathfrak{M}\\cap\\{g=g_0\\}$. In this paper, I will first prove that $v-dim(\\mathfrak{M}_{g_0})=0$. Secondly, I will generalize this formula on 4-manifolds by using a special type of index developed by Jochen Bruning, Robert Seeley, and Fangyun Yang."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.01954","kind":"arxiv","version":3},"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"}