{"paper":{"title":"Hyperbolic rank and subexponential corank of metric spaces","license":"","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Sergei Buyalo, Viktor Schroeder","submitted_at":"2001-02-14T12:33:09Z","abstract_excerpt":"We introduce a new quasi-isometry invariant $\\subcorank X$ of a metric space $X$ called {\\it subexponential corank}. A metric space $X$ has subexponential corank $k$ if roughly speaking there exists a continuous map $g:X\\to T$ such that for each $t\\in T$ the set $g^{-1}(t)$ has subexponential growth rate in $X$ and the topological dimension $\\dim T=k$ is minimal among all such maps. Our main result is the inequality $\\hyprank X\\le\\subcorank X$ for a large class of metric spaces $X$ including all locally compact Hadamard spaces, where $\\hyprank X$ is maximal topological dimension of $\\di Y$ amo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0102109","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"}