{"paper":{"title":"Chern-Simons line bundle on Teichm\\\"uller space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.GT","math.MP"],"primary_cat":"math.DG","authors_text":"Colin Guillarmou, Sergiu Moroianu","submitted_at":"2011-02-09T21:01:52Z","abstract_excerpt":"Let $X$ be a non-compact geometrically finite hyperbolic 3-manifold without cusps of rank 1. The deformation space $\\mc{H}$ of $X$ can be identified with the Teichm\\\"uller space $\\mc{T}$ of the conformal boundary of $X$ as the graph of a section in $T^*\\mc{T}$. We construct a Hermitian holomorphic line bundle $\\mc{L}$ on $\\mc{T}$, with curvature equal to a multiple of the Weil-Petersson symplectic form. This bundle has a canonical holomorphic section defined by $e^{\\frac{1}{\\pi}{\\rm Vol}_R(X)+2\\pi i\\CS(X)}$ where ${\\rm Vol}_R(X)$ is the renormalized volume of $X$ and $\\CS(X)$ is the Chern-Simo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.1981","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"}