{"paper":{"title":"Spectral rigidity of automorphic orbits in free groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.GR","authors_text":"Armando Martino, Ilya Kapovich, Mathieu Carette, Stefano Francaviglia","submitted_at":"2011-06-03T15:40:49Z","abstract_excerpt":"It is well-known that a point $T\\in cv_N$ in the (unprojectivized) Culler-Vogtmann Outer space $cv_N$ is uniquely determined by its \\emph{translation length function} $||.||_T:F_N\\to\\mathbb R$. A subset $S$ of a free group $F_N$ is called \\emph{spectrally rigid} if, whenever $T,T'\\in cv_N$ are such that $||g||_T=||g||_{T'}$ for every $g\\in S$ then $T=T'$ in $cv_N$. By contrast to the similar questions for the Teichm\\\"uller space, it is known that for $N\\ge 2$ there does not exist a finite spectrally rigid subset of $F_N$.\n  In this paper we prove that for $N\\ge 3$ if $H\\le Aut(F_N)$ is a subgr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.0688","kind":"arxiv","version":5},"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"}