{"paper":{"title":"A finite presentation for the automorphism group of the first homology of a non-orientable surface over $\\mathbb Z_2$ preserving the mod $2$ intersection form","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.GT","authors_text":"Genki Omori, Ryoma Kobayashi","submitted_at":"2014-10-27T07:19:55Z","abstract_excerpt":"Let $\\operatorname{Aut}(H_1(N_g;\\mathbb Z_2),\\cdot )$ be the group of automorphisms on the first homology group with $\\mathbb Z_2$ coefficient of a closed non-orientable surface $N_g$ preserving the mod $2$ intersection form. In this paper, we obtain a finite presentation for $\\operatorname{Aut}(H_1(N_g;\\mathbb Z_2),\\cdot )$. As applications we calculate the first homology group and the second homology group of $\\operatorname{Aut}(H_1(N_g;\\mathbb Z_2),\\cdot )$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.7138","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":""},"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"}