{"paper":{"title":"Cohomology of Toroidal Orbifold Quotients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.AT","authors_text":"Alejandro Adem, Ali Nabi Duman, Jose Manuel Gomez","submitted_at":"2010-03-01T19:43:12Z","abstract_excerpt":"Let $\\phi:\\Z/p\\to GL_{n}(\\Z)$ denote an integral representation of the cyclic group of prime order $p$. This induces a $\\Z/p$-action on the torus $X=\\R^{n}/\\Z^{n}$. The goal of this paper is to explicitly compute the cohomology groups $H^{*}(X/\\Z/p;\\Z)$ for any such representation. As a consequence we obtain an explicit calculation of the integral cohomology of the classifying space associated to the family of finite subgroups for any crystallographic group $\\Gamma =\\Z^n\\rtimes\\Z/p$ with prime holonomy."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1003.0435","kind":"arxiv","version":4},"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"}