{"paper":{"title":"Homotopical Height","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.AT","math.SG"],"primary_cat":"math.GT","authors_text":"Dishant Pancholi, Indranil Biswas, Mahan Mj","submitted_at":"2013-02-04T08:03:12Z","abstract_excerpt":"Given a group $G$ and a class of manifolds $\\CC$ (e.g. symplectic, contact, K\\\"ahler etc), it is an old problem to find a manifold $M_G \\in \\CC$ whose fundamental group is $G$. This article refines it: for a group $G$ and a positive integer $r$ find $M_G \\in \\CC$ such that $\\pi_1(M_G)=G$ and $\\pi_i(M_G)=0$ for $1<i<r$. We thus provide a unified point of view systematizing known and new results in this direction for various different classes of manifolds. The largest $r$ for which such an $M_G \\in \\CC$ can be found is called the homotopical height $ht_\\CC(G)$. Homotopical height provides a dime"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.0607","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"}