{"paper":{"title":"Regular Cocycles and Biautomatic Structures","license":"","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Lawrence Reeves, Walter D. Neumann","submitted_at":"1994-11-07T00:00:00Z","abstract_excerpt":"Let $E$ be a virtually central extension of the group $G$ by a finitely generated abelian group $A$.  We show that $E$ carries a biautomatic structure if and only if $G$ has a biautomatic structure $L$ for which the cohomology class of the extension is represented by an $L$-regular cocycle.  Moreover, a cohomology class is $L$-regular if some multiple of it is or if its restriction to some finite index subgroup is.\n  We also show that the entire second cohomology of a Fuchsian group is regular, so any virtually central extension is biautomatic.  In particular, if the fundamental group of a Sei"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9411203","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":""},"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"}