{"paper":{"title":"Metrics and spectral triples for Dirichlet and resistance forms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.DG","math.FA","math.MP","math.PR"],"primary_cat":"math.OA","authors_text":"Alexander Teplyaev, Daniel J. Kelleher, Michael Hinz","submitted_at":"2013-09-23T19:54:33Z","abstract_excerpt":"The article deals with intrinsic metrics, Dirac operators and spectral triples induced by regular Dirichlet and resistance forms. We show, in particular, that if a local resistance form is given and the space is compact in resistance metric, then the intrinsic metric yields a geodesic space. Given a regular Dirichlet form, we consider Dirac operators within the framework of differential 1-forms proposed by Cipriani and Sauvageot, and comment on its spectral properties. If the Dirichlet form admits a carr\\'e operator and the generator has discrete spectrum, then we can construct a related spect"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.5937","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":""},"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"}