{"paper":{"title":"Cohomological rigidity and the number of homeomorphism types for small covers over prisms","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":["math.AT","math.CO"],"primary_cat":"math.GT","authors_text":"Xiangyu Cao, Zhi L\\\"u","submitted_at":"2009-03-23T18:50:36Z","abstract_excerpt":"In this paper, based upon the basic theory for glued manifolds in M.W. Hirsch (1976) \\cite[Chapter 8, \\S 2 Gluing Manifolds Together]{h}, we give a method of constructing homeomorphisms between two small covers over simple convex polytopes. As a result we classify, up to homeomorphism, all small covers over a 3-dimensional prism $P^3(m)$ with $m\\geq 3$. We introduce two invariants from colored prisms and other two invariants from ordinary cohomology rings with ${\\Bbb Z}_2$-coefficients of small covers. These invariants can form a complete invariant system of homeomorphism types of all small co"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0903.3653","kind":"arxiv","version":3},"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"}