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

Ankur Sarkar

doi:10.1007/s12044-025-00829-2

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arXiv · 2502.20736

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

Ankur Sarkar

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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 $M\times\mathbb{S}^k$ for $1\leq k\leq 14$ and classify all smooth manifolds homeomorphic to $M\times\mathbb{S}^k,$ up to concordance for $1\leq k\leq 10.$ Moreover, we provide a diffeomorphism classification of smooth manifolds homeomorphic to $M\times\mathbb{S}^1,$ where $H^4(M;\mathbb{Z})=\mathbb{Z}.$

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BibTeX RIS

Ankur Sarkar. 2025-02-28. Smooth Structures on the product of 3-connected 8-manifolds with spheres. https://doi.org/10.1007/s12044-025-00829-2

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