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arXiv · 2507.23766

Twisted embeddings of tori have small extrinsic systole

Sahana Vasudevan
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Abstract

We prove a type of systolic inequality for embeddings of $T^2$ in $\mathbb{R}^3$. In particular, a highly twisted $T^2$ embedded in $\mathbb{R}^3$ must contain a non-contractible loop of small $\mathbb{R}^3$-diameter.

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Sahana Vasudevan. 2025-07-31. Twisted embeddings of tori have small extrinsic systole. https://arxiv.org/abs/2507.23766

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