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| Main Author: | |
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| Format: | Preprint |
| Published: |
2022
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2203.09433 |
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Table of 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 $|S| \ge 2$.