Smoothing topological pseudo-isotopies of 4-manifolds
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866911072134365184 |
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| author | Orson, Patrick Powell, Mark Randal-Williams, Oscar |
| author_facet | Orson, Patrick Powell, Mark Randal-Williams, Oscar |
| contents | Given a closed, smooth 4-manifold $X$ and self-diffeomorphism $f$ that is topologically pseudo-isotopic to the identity, we study the question of whether $f$ is moreover smoothly pseudo-isotopic to the identity. If the fundamental group of $X$ lies in a certain class, which includes trivial, free, and finite groups of odd order, we show the answer is always affirmative. On the other hand, we produce the first examples of manifolds $X$ and diffeomorphisms $f$ where the answer is negative. Our investigation is motivated by the question, which remains open, of whether there exists a self-diffeomorphism of a closed 4-manifold that is topologically isotopic to the identity, but not stably smoothly isotopic to the identity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_16984 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Smoothing topological pseudo-isotopies of 4-manifolds Orson, Patrick Powell, Mark Randal-Williams, Oscar Geometric Topology 57K40, 57N37, 57R52 Given a closed, smooth 4-manifold $X$ and self-diffeomorphism $f$ that is topologically pseudo-isotopic to the identity, we study the question of whether $f$ is moreover smoothly pseudo-isotopic to the identity. If the fundamental group of $X$ lies in a certain class, which includes trivial, free, and finite groups of odd order, we show the answer is always affirmative. On the other hand, we produce the first examples of manifolds $X$ and diffeomorphisms $f$ where the answer is negative. Our investigation is motivated by the question, which remains open, of whether there exists a self-diffeomorphism of a closed 4-manifold that is topologically isotopic to the identity, but not stably smoothly isotopic to the identity. |
| title | Smoothing topological pseudo-isotopies of 4-manifolds |
| topic | Geometric Topology 57K40, 57N37, 57R52 |
| url | https://arxiv.org/abs/2507.16984 |