Smooth Structures on the product of 3-connected 8-manifolds with spheres
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912520296464384 |
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| author | Sarkar, Ankur |
| author_facet | Sarkar, Ankur |
| contents | 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 $H^4(M;\mathbb{Z})=\mathbb{Z}.$ |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2502_20736 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Smooth Structures on the product of 3-connected 8-manifolds with spheres Sarkar, Ankur Geometric Topology Algebraic Topology 57R55, 57R67, 55P47 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 $H^4(M;\mathbb{Z})=\mathbb{Z}.$ |
| title | Smooth Structures on the product of 3-connected 8-manifolds with spheres |
| topic | Geometric Topology Algebraic Topology 57R55, 57R67, 55P47 |
| url | https://arxiv.org/abs/2502.20736 |