{"paper":{"title":"Achirality of Sol 3-Manifolds, Stevenhagen Conjecture and Shimizu's L-series","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.GT","authors_text":"Shicheng Wang, Ye Tian, Zhongzi Wang","submitted_at":"2024-06-19T06:06:38Z","abstract_excerpt":"A closed orientable manifold is {\\em achiral} if it admits an orientation reversing homeomorphism. A commensurable class of closed manifolds is achiral if it contains an achiral element, or equivalently, each manifold in $\\CM$ has an achiral finite cover.\n  Each commensurable class containing non-orientable elements must be achiral.\n  It is natural to wonder how many\n  commensurable classes are achiral and how many achiral classes have non-orientable elements.\n  We study this problem for Sol 3-manifolds. Each commensurable class $\\CM$ of Sol 3-manifold has a complete topological invariant $D_{"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2406.13241","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/2406.13241/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"}