{"paper":{"title":"On the $\\Sigma$-invariants of generalized Thompson groups and Houghton groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.GR","authors_text":"Matthew C. B. Zaremsky","submitted_at":"2015-02-09T19:33:15Z","abstract_excerpt":"We compute the higher $\\Sigma$-invariants $\\Sigma^m(F_{n,\\infty})$ of the generalized Thompson groups $F_{n,\\infty}$, for all $m,n\\ge 2$. This extends the $n=2$ case done by Bieri, Geoghegan and Kochloukova, and the $m=2$ case done by Kochloukova. Our approach differs from those used in the $n=2$ and $m=2$ cases; we look at the action of $F_{n,\\infty}$ on a $\\textrm{CAT}(0)$ cube complex, and use Morse theory to compute all the $\\Sigma^m(F_{n,\\infty})$.\n  We also obtain lower bounds on $\\Sigma^m(H_n)$, for the Houghton groups $H_n$, again using actions on $\\textrm{CAT}(0)$ cube complexes, and "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.02620","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"}