Free maps in critical dimension on low-dimensional tori and closed surfaces
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866914611418103808 |
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| author | De Leo, Roberto |
| author_facet | De Leo, Roberto |
| contents | We present a method to build free immersions in critical dimension on $m$-tori for $m=2,3,4,5$ by using a factorization trick inspired by tori immersions in critical dimension. As an application, we show that the set of smooth free maps from a closed surface $M$ to \(\mathbb R^5\) is nonempty. In particular, every closed surface embeds freely in \(\mathbb R^5\). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_24610 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Free maps in critical dimension on low-dimensional tori and closed surfaces De Leo, Roberto Geometric Topology Differential Geometry We present a method to build free immersions in critical dimension on $m$-tori for $m=2,3,4,5$ by using a factorization trick inspired by tori immersions in critical dimension. As an application, we show that the set of smooth free maps from a closed surface $M$ to \(\mathbb R^5\) is nonempty. In particular, every closed surface embeds freely in \(\mathbb R^5\). |
| title | Free maps in critical dimension on low-dimensional tori and closed surfaces |
| topic | Geometric Topology Differential Geometry |
| url | https://arxiv.org/abs/2605.24610 |