Enumerating Smooth Structures on $\mathbb{C}P^3\times\mathbb{S}^k$
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866908295460028416 |
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| author | Basu, Samik Kasilingam, Ramesh Sarkar, Ankur |
| author_facet | Basu, Samik Kasilingam, Ramesh Sarkar, Ankur |
| contents | In this paper, we compute the concordance inertia group of the product $M \times \mathbb{S}^k$, where $M$ is a simply connected, closed, smooth 6-manifold, for $1 \leq k \leq 10$, using known low-dimensional computations of the stable homotopy groups of spheres. Specifically, for $M = \mathbb{C}P^3$, we determine the inertia group of $\mathbb{C}P^3 \times \mathbb{S}^k$ for $2 \leq k \leq 7, k \neq 6$, and establish a diffeomorphism classification of all smooth manifolds homeomorphic to $\mathbb{C}P^3 \times \mathbb{S}^k$ for $1 \leq k \leq 7$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_16267 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Enumerating Smooth Structures on $\mathbb{C}P^3\times\mathbb{S}^k$ Basu, Samik Kasilingam, Ramesh Sarkar, Ankur Algebraic Topology Geometric Topology Primary : 57R55, 55P42, Secondary : 57R65, 55Q45 In this paper, we compute the concordance inertia group of the product $M \times \mathbb{S}^k$, where $M$ is a simply connected, closed, smooth 6-manifold, for $1 \leq k \leq 10$, using known low-dimensional computations of the stable homotopy groups of spheres. Specifically, for $M = \mathbb{C}P^3$, we determine the inertia group of $\mathbb{C}P^3 \times \mathbb{S}^k$ for $2 \leq k \leq 7, k \neq 6$, and establish a diffeomorphism classification of all smooth manifolds homeomorphic to $\mathbb{C}P^3 \times \mathbb{S}^k$ for $1 \leq k \leq 7$. |
| title | Enumerating Smooth Structures on $\mathbb{C}P^3\times\mathbb{S}^k$ |
| topic | Algebraic Topology Geometric Topology Primary : 57R55, 55P42, Secondary : 57R65, 55Q45 |
| url | https://arxiv.org/abs/2503.16267 |