{"paper":{"title":"A generalization of Seifert geometry based on the Siegel upper half-space","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.GT","authors_text":"Qing Lan","submitted_at":"2025-01-09T13:54:21Z","abstract_excerpt":"The Seifert geometry, $\\widetilde{\\mathrm{SL}(2,\\mathbb{R})}$-geometry, is one of Thurston's eight $3$-dimensional geometries. It fibers over the hyperbolic plane $\\mathbb{H}^2$, which is a special case of the Siegel upper half-space $\\mathrm{Sp}(2n,\\mathbb{R})\\curvearrowright {\\mathfrak{H}}_n$. In this paper we construct an analogous geometry fibering over the Siegel upper half-space, and provide a volume formula for some manifolds with this geometry. For $n=2$, a prototype is constructed via the normal bundle of an equivariant embedding into a Grassmannian manifold. It turns out that this ge"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.05245","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2501.05245/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"}