2014/11/12 by Gregory R. Schneider, Schneider, Gregory R.
Mathematics · #57R17 (Primary) 57M25 (Secondary) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals
paper · pdf · doi:10.48550/arxiv.1411.3090
openalex publication_date 2014/11/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We show that under certain conditions the flyping operation on rational tangles, which produces topologically isotopic tangles, may also produce tangles which are not Legendrian isotopic when viewed in the standard contact structure on ℝ3. This work is motivated by questions posed by Traynor, and incorporates techniques inspired by work of Eliashberg and Fraser. The proofs within employ a new method of diagramming rational tangles which is also used to easily describe the characteristic foliations of compressing discs for their complements.