{"paper":{"title":"A new construction of lens spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Dong Youp Suh, Soumen Sarkar","submitted_at":"2013-04-17T14:23:40Z","abstract_excerpt":"Let $T^n$ be the real $n$-torus group. We give a new definition of lens spaces and study the diffeomorphic classification of lens spaces. We show that any $3$-dimensional lens space $L(p; q)$ is $T^2$-equivariantly cobordant to zero. We also give some sufficient conditions for higher dimensional lens spaces $L(p; q_1, \\ldots, q_n)$ to be $T^{n+1}$-equivariantly cobordant to zero. In 2005, B. Hanke showed that complex equivariant cobordism class of a lens space is trivial. Nevertheless, our proofs are constructive using toric topological arguments."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.4836","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"}