{"paper":{"title":"The classification of smooth structures on a homotopy complex projective space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Ramesh Kasilingam","submitted_at":"2015-10-11T10:02:52Z","abstract_excerpt":"We classify, up to diffeomorphism, all closed smooth manifolds homeomorphic to the complex projective $n$-space $\\mathbb{C}\\textbf{P}^n$, where $n=3$ and $4$. Let $M^{2n}$ be a closed smooth $2n$-manifold homotopy equivalent to $\\mathbb{C}\\textbf{P}^n$. We show that, up to diffeomorphism, $M^{6}$ has a unique differentiable structure and $M^{8}$ has at most two distinct differentiable structures. We also show that, up to concordance, there exist at least two distinct differentiable structures on a finite sheeted cover $N^{2n}$ of $\\mathbb{C}\\textbf{P}^n$ for $n=4, 7$ or $8$ and six distinct di"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.03032","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"}