2000/04/28 by Hugh Howards, John Luecke, Howards, Hugh +1
Computer Science · Mathematics · #57M25 #Advanced Combinatorial Mathematics #Computational Geometry and Mesh Generation #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #math.GT #msc:57M25
paper · pdf · doi:10.48550/arxiv.math/0004183
10 pages, 3 figures
arxiv created 2000/04/28 · openalex publication_date 2000/04/28 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A knot k is called ``strongly (n-1)-trivial.'' if there exists a projection of k, such that one can choose n crossings of the projection with the property that making the crossing changes corresponding to any of the 2n-1 nontrivial combinations of the selected crossings turns the original knot into the unknot. We prove that given any non-trivial knot k of genus g, k fails to be strongly n-trivial for all n, n ≥ 3g-1.