2017/09/25 by Christopher William Davis, Matthias Nagel, Davis, Christopher William +5
Computer Science · Mathematics · #57M25 #Computational Geometry and Mesh Generation #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #math.GT #msc:57M25
paper · pdf · doi:10.48550/arxiv.1709.08478
37 pages, 14 figures
arxiv created 2017/09/25 · openalex publication_date 2017/09/25 · arxiv updated 2017/09/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We give a refined value group for the collection of triple linking numbers of links in the 3-sphere. Given two links with the same pairwise linking numbers we show that they have the same refined triple linking number collection if and only if the links admit homeomorphic surface systems. Moreover these two conditions hold if and only if the link exteriors are bordant over B ℤn, and if and only if the third lower central series quotients π/π3 of the link groups are isomorphic preserving meridians and longitudes. We also show that these conditions imply that the link groups have isomorphic fourth lower central series quotients π/π4, preserving meridians.