{"paper":{"title":"Geometric Intersection Number and analogues of the Curve Complex for free groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.GR","authors_text":"Ilya Kapovich, Martin Lustig","submitted_at":"2007-11-24T01:43:24Z","abstract_excerpt":"For the free group $F_{N}$ of finite rank $N \\geq 2$ we construct a canonical Bonahon-type continuous and $Out(F_N)$-invariant \\emph{geometric intersection form} \\[ <, >: \\bar{cv}(F_N)\\times Curr(F_N)\\to \\mathbb R_{\\ge 0}. \\]\n  Here $\\bar{cv}(F_N)$ is the closure of unprojectivized Culler-Vogtmann's Outer space $cv(F_N)$ in the equivariant Gromov-Hausdorff convergence topology (or, equivalently, in the length function topology). It is known that $\\bar{cv}(F_N)$ consists of all \\emph{very small} minimal isometric actions of $F_N$ on $\\mathbb R$-trees. The projectivization of $\\bar{cv}(F_N)$ pro"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0711.3806","kind":"arxiv","version":4},"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"}