{"paper":{"title":"Rigidity and Vanishing Theorems on ${\\mathbb{Z}}/k$ Spin$^c$ manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.DG","authors_text":"Bo Liu, Jianqing Yu","submitted_at":"2011-04-20T08:49:16Z","abstract_excerpt":"In this paper, we first establish an $S^1$-equivariant index theorem for Spin$^c$ Dirac operators on $\\mathbb{Z}/k$ manifolds, then combining with the methods developed by Taubes \\cite{MR998662} and Liu-Ma-Zhang \\cite{MR1870666,MR2016198}, we extend Witten's rigidity theorem to the case of $\\mathbb{Z}/k$ Spin$^c$ manifolds. Among others, our results resolve a conjecture of Devoto \\cite{MR1405063}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.3972","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"}