2021/10/06 by William C. Stagner, Stagner, William
Mathematics · #57K30 #Advanced Combinatorial Mathematics #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2110.02936
openalex publication_date 2021/10/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
M. Freedman and V. Krushkal introduced the notion of a "filling" link in a 3-manifold: a link L is filling in M if for any spine G of M disjoint from L, π1(G) injects into π1(M ∖ L ). Freedman and Krushkal show that there exist links in the 3-torus T3 that satisfy a weaker form of filling, but they leave open the question of whether T3 contains an actual filling link. We answer this question affirmatively by proving in fact that every closed, orientable 3-manifold M with rank(π1(M)) = 3 contains a filling link.