Smooth structures on ℂP^m for 5≤ m≤ 8

2017/01/26 by Ramesh Kasilingam, Kasilingam, Ramesh
Computer Science · Mathematics · #55P42 #57R55 #57R60 #57R67 #Advanced Topology and Set Theory #FOS: Mathematics #Geometric Topology (math.GT) #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.1701.07592

openalex publication_date 2017/01/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We classify up to diffeomorphism all smooth manifolds homeomorphic to the complex projective m-space ℂP^m for m = 5, 6, 7 and 8. As an application, for m = 7 and 8, we compute the smooth tangential structure set of ℂP^m and obtain a bound on the number of smooth homotopy complex projective m-spaces with given Pontryagin classes up to orientation-preserving diffeomorphism. We also show that there exists a smooth manifold which is tangentially homotopy equivalent but not homeomorphic to ℂP⁸.

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