{"paper":{"title":"Inflexibility, Weil-Petersson distance, and volumes of fibered 3-manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Jeffrey Brock, Kenneth Bromberg","submitted_at":"2014-12-01T23:33:02Z","abstract_excerpt":"A recent preprint of S. Kojima and G. McShane [KM] observes a beautiful explicit connection between Teichm\\\"uller translation distance and hyperbolic volume. It relies on a key estimate which we supply here: using geometric inflexibility of hyperbolic 3-manifolds, we show that for $S$ a closed surface, and $\\psi \\in \\text{Mod}(S)$ pseudo-Anosov, the double iteration $Q(\\psi^{-n}(X),\\psi^n(X))$ has convex core volume differing from $2n \\text{vol}(M_\\psi)$ by a uniform additive constant, where $M_\\psi$ is the hyperbolic mapping torus for $\\psi$. We combine this estimate with work of Schlenker, a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.0733","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"}