{"paper":{"title":"Quotient and blow-up of automorphisms of graphs of groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Kaidi Ye","submitted_at":"2015-12-02T01:51:23Z","abstract_excerpt":"In this paper we study the quotient and \"blow-up\" of graph-of-groups $\\cal{G}$ and of their automorphisms $H: \\cal{G} \\rightarrow \\cal{G}$. We show that the existence of such a \"blow-up\" of $\\bar{H}: \\bar{\\cal{G}} \\rightarrow \\bar{\\cal{G}}$ relative to a given family of \"local\" graph-of-groups isomorphisms $H_{i}: \\cal{G}_{i} \\rightarrow \\cal{G}_{i}$ depends crucially on the $H_{i}$-conjugacy class of the correction term $\\delta(\\bar{E}_{i})$ for any edge $\\bar{E}_{i}$ of $\\bar{\\cal{G}}$, where $H$-congjugacy is a new but natural concept introduced here. As an application we obtain a criterion"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.00542","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"}