Skew loops in flat tori

2007/01/31 by Bruce Solomon, Solomon, Bruce
Mathematics · #53A04 #Advanced Combinatorial Mathematics #Differential Geometry (math.DG) #FOS: Mathematics #History and Theory of Mathematics #Mathematics and Applications #math.DG #msc:53A04

paper · pdf · doi:10.48550/arxiv.math/0701913

openalex publication_date 2007/01/31 · arxiv created 2007/07/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 Rⁿ. 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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