Classification of real rational knots of low degree in the 3-sphere

2013/11/15 by Shane D’Mello, Shane D'Mello, D'Mello, Shane
Mathematics · #14H50 #14P25 #57M25 #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #math.GT #msc:14H50 #msc:14P25 #msc:57M25

paper · pdf · doi:10.48550/arxiv.1311.3996

26 pages

arxiv created 2013/11/15 · openalex publication_date 2013/11/15 · arxiv updated 2013/11/19 · openalex created_date 2016/08/23 · openalex updated_date 2026/07/28

Abstract

In this paper we classify, up to rigid isotopy, non-singular real rational curves of degrees less than or equal to 6 in a quadric homeomorphic to the 3-sphere. We also study their connections with rigid isotopy classes of real rational knots in \mathbbRP³.

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