A topologically extendible mapping class that is not smoothly extendible
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866916796604350464 |
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| author | Lawande, Shital Saha, Kuldeep |
| author_facet | Lawande, Shital Saha, Kuldeep |
| contents | We give an example of a smooth characteristic embedding of a torus in $\s^2 \times \s^2 \# \s^1 \times \s^3$ such that there exists no diffeomorphism of the ambient $4$-manifold that induces the Dehn twist along a meridian of the torus, but there exists a homeomorphism of the ambient $4$-manifold, isotopic to identity, that induces the Dehn twist. As an application of our methods, we provide examples of two proper smooth embeddings of an annulus in $\s^2 \times \s^2 \# \s^1 \times \s^3 \setminus int(\D^4)$ which are topologically isotopic, but not smoothly isotopic (relative to boundary). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_23999 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A topologically extendible mapping class that is not smoothly extendible Lawande, Shital Saha, Kuldeep Geometric Topology 57R52, 57K20 (Primary) 57R15 (Secondary) We give an example of a smooth characteristic embedding of a torus in $\s^2 \times \s^2 \# \s^1 \times \s^3$ such that there exists no diffeomorphism of the ambient $4$-manifold that induces the Dehn twist along a meridian of the torus, but there exists a homeomorphism of the ambient $4$-manifold, isotopic to identity, that induces the Dehn twist. As an application of our methods, we provide examples of two proper smooth embeddings of an annulus in $\s^2 \times \s^2 \# \s^1 \times \s^3 \setminus int(\D^4)$ which are topologically isotopic, but not smoothly isotopic (relative to boundary). |
| title | A topologically extendible mapping class that is not smoothly extendible |
| topic | Geometric Topology 57R52, 57K20 (Primary) 57R15 (Secondary) |
| url | https://arxiv.org/abs/2505.23999 |