{"paper":{"title":"The index of Toeplitz operators on compact Lie groups and simply connected closed 3-manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Duv\\'an Cardona","submitted_at":"2018-09-27T08:31:57Z","abstract_excerpt":"In this paper we use the notion of operator-valued symbol in order to compute the index of Toeplitz operators on compact Lie groups. Our approach combines the Connes index theorem and the infinite-dimensional operator-valued symbolic calculus of Ruzhansky-Turunen. We also give applications to the index of Toeplitz operators on simply connected closed $3$-manifolds $\\mathbb{M}\\simeq \\mathbb{S}^3\\simeq \\textnormal{SU}(2) ,$ by using, as a fundamental tool, the Poincar\\'e theorem (see Perelman [31,32,33,34])"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.10401","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"}