{"paper":{"title":"On locally constructible spheres and balls","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.AT","math.MG"],"primary_cat":"math.CO","authors_text":"Bruno Benedetti, G\\\"unter M. Ziegler","submitted_at":"2009-02-03T07:15:19Z","abstract_excerpt":"Durhuus and Jonsson (1995) introduced the class of \"locally constructible\" (LC) 3-spheres and showed that there are only exponentially-many combinatorial types of simplicial LC 3-spheres. Such upper bounds are crucial for the convergence of models for 3D quantum gravity.\n  We characterize the LC property for d-spheres (\"the sphere minus a facet collapses to a (d-2)-complex\") and for d-balls. In particular, we link it to the classical notions of collapsibility, shellability and constructibility, and obtain hierarchies of such properties for simplicial balls and spheres. The main corollaries fro"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0902.0436","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"}