Exotic diffeomorphisms on $4$-manifolds with $b_2^+ = 2$
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866912022119055360 |
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| author | Qiu, Haochen |
| author_facet | Qiu, Haochen |
| contents | While the exotic diffeomorphisms turned out to be very rich, we know much less about the $b^+_2 =2$ case, as parameterized gauge-theoretic invariants are not well defined. In this paper we present a method (that is, comparing the winding number of parameter families) to find exotic diffeomorphisms on simply-connected smooth closed $4$-manifolds with $b^+_2 =2$, and as a result we obtain that $2\mathbb{C}\mathbb{P}^2 \# 10 (-{\mathbb{C}\mathbb{P}^2})$ admits exotic diffeomorphisms. This is currently the smallest known example of a closed $4$-manifold that supports exotic diffeomorphisms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_07009 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Exotic diffeomorphisms on $4$-manifolds with $b_2^+ = 2$ Qiu, Haochen Geometric Topology While the exotic diffeomorphisms turned out to be very rich, we know much less about the $b^+_2 =2$ case, as parameterized gauge-theoretic invariants are not well defined. In this paper we present a method (that is, comparing the winding number of parameter families) to find exotic diffeomorphisms on simply-connected smooth closed $4$-manifolds with $b^+_2 =2$, and as a result we obtain that $2\mathbb{C}\mathbb{P}^2 \# 10 (-{\mathbb{C}\mathbb{P}^2})$ admits exotic diffeomorphisms. This is currently the smallest known example of a closed $4$-manifold that supports exotic diffeomorphisms. |
| title | Exotic diffeomorphisms on $4$-manifolds with $b_2^+ = 2$ |
| topic | Geometric Topology |
| url | https://arxiv.org/abs/2409.07009 |