{"paper":{"title":"Index realization for automorphisms of free groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Martin Lustig, Thierry Coulbois","submitted_at":"2015-06-15T09:55:44Z","abstract_excerpt":"For any surface $\\Sigma$ of genus $g \\geq 1$ and (essentially) any collection of positive integers $i_1, i_2, \\ldots, i_\\ell$ with $i_1+\\cdots +i_\\ell = 4g-4$ Masur and Smillie have shown that there exists a pseudo-Anosov homeomorphism $h:\\Sigma \\to \\Sigma$ with precisely $\\ell$ singularities $S_1, \\ldots, S_\\ell$ in its stable foliation $\\cal L$, such that $\\cal L$ has precisely $i_k+2$ separatrices raying out from each $S_k$.\n  In this paper we prove the analogue of this result for automorphisms of a free group $F_N$, where \"pseudo-Anosov homeomorphism\" is replaced by \"fully irreducible auto"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.04536","kind":"arxiv","version":3},"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"}