{"paper":{"title":"3d spectral networks and classical Chern-Simons theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.AT","math.GT"],"primary_cat":"math.DG","authors_text":"Andrew Neitzke, Daniel S. Freed","submitted_at":"2022-08-15T19:55:48Z","abstract_excerpt":"We define the notion of spectral network on manifolds of dimension $\\le 3$. For a manifold $X$ equipped with a spectral network, we construct equivalences between Chern-Simons invariants of flat ${\\mathrm {SL}}(2,{\\mathbb C})$-bundles over $X$ and Chern-Simons invariants of flat ${\\mathbb C}^\\times$-bundles over ramified double covers $\\widetilde X$. Applications include a new viewpoint on dilogarithmic formulas for Chern-Simons invariants of flat ${\\mathrm {SL}}(2,{\\mathbb C})$-bundles over triangulated 3-manifolds, and an explicit description of Chern-Simons lines of flat ${\\mathrm {SL}}(2,{"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2208.07420","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2208.07420/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}