{"paper":{"title":"Dual automorphisms of free groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Fedaa Ibrahim, Martin Lustig","submitted_at":"2013-06-24T18:07:06Z","abstract_excerpt":"For any choice of a basis $\\cal A$ the free group $F_N$ of finite rank $N \\geq 2$ can be canonically identified with the set $F(\\cal A)$ of reduced words in $\\cal A\\cup \\cal A^{-1}$. However, such a word $w \\in F(\\cal A)$ admits a second interpretation, namely as cylinder $C^1_w \\subset \\partial F_N$. The subset of $\\partial F_N$ defined by $C^1_w$ depends not only on the element of $F_N$ given by the word $w$, but also on the chosen basis $\\cal A$. In particular one has in general, for $\\Phi \\in \\Aut(F_N)$: $$\\Phi(C^1_w) \\neq C^1_{\\Phi(w)}$$ Indeed, the image of a cylinder under an automorphi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.5696","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"}