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arXiv · 2605.24610

Free maps in critical dimension on low-dimensional tori and closed surfaces

Roberto De Leo
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Abstract

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 \(\mathbb R^5\).

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Roberto De Leo. 2026-05-27. Free maps in critical dimension on low-dimensional tori and closed surfaces. https://arxiv.org/abs/2605.24610

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