vix.ing · top · new · best · stats · spec

(4,-(2n+5))-torus knot with only 1 normal ruling

2015/12/26 by Watchareepan Atiponrat, Atiponrat, Watchareepan
Engineering · Mathematics · #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Metal Forming Simulation Techniques

paper · pdf · doi:10.48550/arxiv.1512.08057

openalex publication_date 2015/12/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The main purpose of this paper is to provide an infinite family of counter examples of the open problem mentioned in [2]. In particular, we present an infinite family of a particular Legendrian (4,-(2n+5))-torus knot, for each n ≥ 0, which has only 1 normal ruling, but do not satisfy the even number of clasps condition of Theorem 3 of [2]. Thus, these normal rulings cannot imply the existence of a decomposable exact Lagrandian filling.

Related