Diffeotopy groups of non-compact 4-manifolds
Fuente:
arXiv
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2022
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866916288938377216 |
|---|---|
| author | Nonino, Isacco |
| author_facet | Nonino, Isacco |
| contents | We provide information on diffeotopy groups of exotic smoothings of punctured 4-manifolds, extending previous results on diffeotopy groups of exotic $\mathbb{R}^4$'s. In particular, we prove that for a smoothable 4-manifold $M$ and for a non-empty, discrete set of points $S \subsetneq \mathring{M}$, there are uncountably many distinct smoothings of $M\smallsetminus S$ whose diffeotopy groups are uncountable.
We then prove that for a smoothable 4-manifold $M$ and for a non-empty, discrete set of points $S \subsetneq \mathring{M}$, there exists a smoothing of $M\smallsetminus S$ whose diffeotopy groups have similar properties as $\mathcal{R}_U$, Freedman and Taylor's universal $\mathbb{R}^4$.
Moreover, we prove that if $M$ is non-smoothable, both results still hold under the assumption that $|S| \ge 2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2203_09433 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Diffeotopy groups of non-compact 4-manifolds Nonino, Isacco Geometric Topology 57R50, 57S05, 20F38, 57R55, 57K40 We provide information on diffeotopy groups of exotic smoothings of punctured 4-manifolds, extending previous results on diffeotopy groups of exotic $\mathbb{R}^4$'s. In particular, we prove that for a smoothable 4-manifold $M$ and for a non-empty, discrete set of points $S \subsetneq \mathring{M}$, there are uncountably many distinct smoothings of $M\smallsetminus S$ whose diffeotopy groups are uncountable. We then prove that for a smoothable 4-manifold $M$ and for a non-empty, discrete set of points $S \subsetneq \mathring{M}$, there exists a smoothing of $M\smallsetminus S$ whose diffeotopy groups have similar properties as $\mathcal{R}_U$, Freedman and Taylor's universal $\mathbb{R}^4$. Moreover, we prove that if $M$ is non-smoothable, both results still hold under the assumption that $|S| \ge 2$. |
| title | Diffeotopy groups of non-compact 4-manifolds |
| topic | Geometric Topology 57R50, 57S05, 20F38, 57R55, 57K40 |
| url | https://arxiv.org/abs/2203.09433 |