Smooth Structures on M×\mathbbS^k

2024/02/29 by Basu, Samik, Kasilingam, Ramesh, Sarkar, Ankur
#55P42 (Primary) 57R65 #55Q45 (Secondary) #57R55 #Algebraic Topology (math.AT) #FOS: Mathematics

paper · doi:10.48550/arxiv.2402.18914

Abstract

This paper explores various differentiable structures on the product manifold M × \mathbbS^k, where M is either a 4-dimensional closed, oriented, smooth manifold or a simply connected 5-dimensional closed, smooth manifold. We identify the possible stable homotopy types of M and use it to calculate the concordance inertia group and the concordance structure set of M×\mathbbS^k for 1≤ k≤ 10. These calculations enable us to further classify all manifolds that are homeomorphic to ℂP²×\mathbbS^k, up to diffeomorphism, for each 4≤ k≤ 6.

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