{"paper":{"title":"Geometric entropy of geodesic currents on free groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.GT"],"primary_cat":"math.GR","authors_text":"Ilya Kapovich, Tatiana Nagnibeda","submitted_at":"2008-10-26T23:22:19Z","abstract_excerpt":"A \\emph{geodesic current} on a free group $F$ is an $F$-invariant measure on the set $\\partial^2 F$ of pairs of distinct points of $\\partial F$. The space of geodesic currents on $F$ is a natural companion of Culler-Vogtmann's Outer space $cv(F)$ and studying them together yields new information about both spaces as well as about the group $Out(F)$. The main aim of this paper is to introduce and study the notion of {\\it geometric entropy} $h_T(\\mu)$ of a geodesic current $\\mu$ with respect to a point $T$ of $cv(F)$, which can be viewed as a length function on $F$. The geometric entropy is defi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0810.4728","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"}