{"paper":{"title":"The Gauss-Bonnet Theorem for Noncommutative Two Tori With a General Conformal Structure","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA"],"primary_cat":"math.OA","authors_text":"Farzad Fathizadeh, Masoud Khalkhali","submitted_at":"2010-05-26T20:54:42Z","abstract_excerpt":"In this paper we give a proof of the Gauss-Bonnet theorem of Connes and Tretkoff for noncommutative two tori $\\mathbb{T}_{\\theta}^2$ equipped with an arbitrary translation invariant complex structure. More precisely, we show that for any complex number $\\tau$ in the upper half plane, representing the conformal class of a metric on $\\mathbb{T}_{\\theta}^2$, and a Weyl factor given by a positive invertible element $k \\in C^{\\infty}(\\mathbb{T}_{\\theta}^2)$, the value at the origin, $\\zeta (0)$, of the spectral zeta function of the Laplacian $\\triangle'$ attached to $(\\mathbb{T}_{\\theta}^2, \\tau, k"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1005.4947","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"}