Stably exotic 4-manifolds
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915530248552448 |
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| author | Kasprowski, Daniel Powell, Mark |
| author_facet | Kasprowski, Daniel Powell, Mark |
| contents | A pair of closed, smooth $4$-manifolds $M$ and $M'$ are stably exotic if they are stably homeomorphic but not stably diffeomorphic, where stabilisation refers to connected sum with copies of $S^2 \times S^2$. Orientable stable exotica do not exist by a result of Gompf, but Kreck showed that nonorientable examples are plentiful. We investigate which values of the fundamental group $π$ and the first and second Stiefel-Whitney classes $w_1$ and $w_2$ admit stably exotic pairs, providing a complete description if $H_5(π;\mathbb{Z})=0$. In particular we produce new stable exotica, and new settings in which they do not arise. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2508_10499 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Stably exotic 4-manifolds Kasprowski, Daniel Powell, Mark Geometric Topology A pair of closed, smooth $4$-manifolds $M$ and $M'$ are stably exotic if they are stably homeomorphic but not stably diffeomorphic, where stabilisation refers to connected sum with copies of $S^2 \times S^2$. Orientable stable exotica do not exist by a result of Gompf, but Kreck showed that nonorientable examples are plentiful. We investigate which values of the fundamental group $π$ and the first and second Stiefel-Whitney classes $w_1$ and $w_2$ admit stably exotic pairs, providing a complete description if $H_5(π;\mathbb{Z})=0$. In particular we produce new stable exotica, and new settings in which they do not arise. |
| title | Stably exotic 4-manifolds |
| topic | Geometric Topology |
| url | https://arxiv.org/abs/2508.10499 |