Skew loops in flat tori

Bruce Solomon

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Skew loops in flat tori

Bruce Solomon

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Abstract

We produce skew loops -- loops having no pair of parallel tangent lines -- homotopic to any loop in a flat torus or other quotient of R^n. The interesting case here is n=3. More subtly for any n, we characterize the homotopy classes that will contain a skew loop having a specified loop in the unit sphere as tangent indicatrix.

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Bruce Solomon. 2007-07-01. Skew loops in flat tori. https://arxiv.org/abs/math/0701913

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