Twisted embeddings of tori have small extrinsic systole

2025/07/31 by Vasudevan, Sahana · 1 citation
#Differential Geometry (math.DG) #FOS: Mathematics #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.2507.23766

Abstract

We prove a type of systolic inequality for embeddings of T² in ℝ³. In particular, a highly twisted T² embedded in ℝ³ must contain a non-contractible loop of small ℝ³-diameter.

Citations

• Extrinsic systole of Seifert surfaces and distortion of knots
• Metaphors in systolic geometry
• Generalized degree and optimal Loewner-type inequalities
• An optimal Loewner-type systolic inequality and harmonic one-forms of constant norm
• Stable systolic inequalities and cohomology products

Cited by

• Extrinsic systole of Seifert surfaces and distortion of knots

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