The Whitehead group and stably trivial $G$-smoothings
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915269079728128 |
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| author | Wang, Oliver H. |
| author_facet | Wang, Oliver H. |
| contents | A closed manifold $M$ of dimension at least $5$ has only finitely many smooth structures. Moreover, smooth structures of $M$ are in bijection with smooth structures of $M\times\mathbb{R}$. Both of these statements are false equivariantly. In this paper, we use controlled $h$-cobordisms to construct infinitely many $G$-smoothings of a $G$-manifold $X$. Moreover, these $G$-smoothings are isotopic after taking a product with $\mathbb{R}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_00646 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Whitehead group and stably trivial $G$-smoothings Wang, Oliver H. Geometric Topology Algebraic Topology K-Theory and Homology A closed manifold $M$ of dimension at least $5$ has only finitely many smooth structures. Moreover, smooth structures of $M$ are in bijection with smooth structures of $M\times\mathbb{R}$. Both of these statements are false equivariantly. In this paper, we use controlled $h$-cobordisms to construct infinitely many $G$-smoothings of a $G$-manifold $X$. Moreover, these $G$-smoothings are isotopic after taking a product with $\mathbb{R}$. |
| title | The Whitehead group and stably trivial $G$-smoothings |
| topic | Geometric Topology Algebraic Topology K-Theory and Homology |
| url | https://arxiv.org/abs/2505.00646 |