Enumerating Smooth Structures on ℂP³×\mathbbS^k

2025/03/20 by Basu, Samik, Kasilingam, Ramesh, Sarkar, Ankur
#55P42 #55Q45 #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric Topology (math.GT) #Primary : 57R55 #Secondary : 57R65

paper · doi:10.48550/arxiv.2503.16267

Abstract

In this paper, we compute the concordance inertia group of the product M × \mathbbS^k, where M is a simply connected, closed, smooth 6-manifold, for 1 ≤ k ≤ 10, using known low-dimensional computations of the stable homotopy groups of spheres. Specifically, for M = ℂP³, we determine the inertia group of ℂP³ × \mathbbS^k for 2 ≤ k ≤ 7, k ≠ 6, and establish a diffeomorphism classification of all smooth manifolds homeomorphic to ℂP³ × \mathbbS^k for 1 ≤ k ≤ 7.

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