Smooth Structures on the product of 3-connected 8-manifolds with spheres

2025/02/28 by Sarkar, Ankur
#55P47 #57R55 #57R67 #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.2502.20736

Abstract

Let M be a closed, 3-connected, 8-dimensional smooth manifold. In this paper, we compute the concordance inertia group of the product manifold M×\mathbbS^k for 1≤ k≤ 14 and classify all smooth manifolds homeomorphic to M×\mathbbS^k, up to concordance for 1≤ k≤ 10. Moreover, we provide a diffeomorphism classification of smooth manifolds homeomorphic to M×\mathbbS¹, where H⁴(M;ℤ)=ℤ.

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