{"paper":{"title":"Quasi-automorphisms of the infinite rooted 2-edge-coloured binary tree","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Brita E. A. Nucinkis, Simon St John-Green","submitted_at":"2014-12-24T17:16:29Z","abstract_excerpt":"We study the group $QV$, the self-maps of the infinite $2$-edge coloured binary tree which preserve the edge and colour relations at cofinitely many locations. We introduce related groups $QF$, $QT$, $\\tilde{Q}T$, and $\\tilde{Q}V$, prove that $QF$, $\\tilde{Q}T$, and $\\tilde{Q}V$ are of type $\\mathrm{F}_\\infty$, and calculate finite presentations for them. We calculate the normal subgroup structure and rational homology of all $5$ groups, the Bieri--Neumann--Strebel--Renz invariants of $QF$, and discuss the relationship of all $5$ groups with other generalisations of Thompson's groups."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.7715","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"}