{"paper":{"title":"The Boundary at Infinity of the Curve Complex and the Relative Teichm\\\"{u}ller Space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Erica Klarreich","submitted_at":"2018-03-27T21:52:04Z","abstract_excerpt":"In this paper we study the boundary at infinity of the curve complex $\\mathcal{C}(S)$ of a surface $S$ of finite type and the relative Teichm\\\"{u}ller space $\\mathcal{T}_{el}(S)$ obtained from the Teichm\\\"{u}ller space by collapsing each region where a simple closed curve is short to be a set of diameter 1. $\\mathcal{C}(S)$ and $\\mathcal{T}_{el}(S)$ are quasi-isometric, and Masur-Minsky have shown that $\\mathcal{C}(S)$ and $\\mathcal{T}_{el}(S)$ are hyperbolic in the sense of Gromov. We show that the boundary at infinity of $\\mathcal{C}(S)$ and $\\mathcal{T}_{el}(S)$ is the space of topological "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.10339","kind":"arxiv","version":1},"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"}