Smooth Structures on $M\times\mathbb{S}^k$
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866918234800783360 |
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| author | Basu, Samik Kasilingam, Ramesh Sarkar, Ankur |
| author_facet | Basu, Samik Kasilingam, Ramesh Sarkar, Ankur |
| contents | This paper explores various differentiable structures on the product manifold $M \times \mathbb{S}^k$, where $M$ is either a 4-dimensional closed, oriented, smooth manifold or a simply connected 5-dimensional closed, smooth manifold. We identify the possible stable homotopy types of $M$ and use it to calculate the concordance inertia group and the concordance structure set of $M\times\mathbb{S}^k$ for $1\leq k\leq 10$. These calculations enable us to further classify all manifolds that are homeomorphic to $\mathbb{C}P^2\times\mathbb{S}^k$, up to diffeomorphism, for each $4\leq k\leq 6$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_18914 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Smooth Structures on $M\times\mathbb{S}^k$ Basu, Samik Kasilingam, Ramesh Sarkar, Ankur Algebraic Topology 57R55, 55P42 (Primary) 57R65, 55Q45 (Secondary) This paper explores various differentiable structures on the product manifold $M \times \mathbb{S}^k$, where $M$ is either a 4-dimensional closed, oriented, smooth manifold or a simply connected 5-dimensional closed, smooth manifold. We identify the possible stable homotopy types of $M$ and use it to calculate the concordance inertia group and the concordance structure set of $M\times\mathbb{S}^k$ for $1\leq k\leq 10$. These calculations enable us to further classify all manifolds that are homeomorphic to $\mathbb{C}P^2\times\mathbb{S}^k$, up to diffeomorphism, for each $4\leq k\leq 6$. |
| title | Smooth Structures on $M\times\mathbb{S}^k$ |
| topic | Algebraic Topology 57R55, 55P42 (Primary) 57R65, 55Q45 (Secondary) |
| url | https://arxiv.org/abs/2402.18914 |