1-domination of knots

2015/11/22 by Michel Boileau, Boileau, Michel, Steven Boyer +5 · 2 citations
Computer Science · Mathematics · #Algebraic Topology (math.AT) #Combinatorics #Degree (music) #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Knot (papermaking) #Materials science #Mathematics #Physics #math.AT #math.GT #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.1511.07073

published in arXiv (Cornell University) (Cornell University)

arxiv created 2015/11/22 · openalex publication_date 2015/11/22 · arxiv updated 2015/11/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We say that a knot k₁ in the 3-sphere \it 1-dominates another k₂ if there is a proper degree 1 map E(k₁) → E(k₂) between their exteriors, and write k₁ ≥ k₂. When k₁ ≥ k₂ but k₁ ≠ k₂ we write k₁ > k₂. One expects in the latter eventuality that k₁ is more \it complicated. In this paper we produce various sorts of evidence to support this philosophy.

Citations

• Non-zero degree maps between 2n-manifolds
• Epimorphisms between 2–bridge link groups
• Orderable 3-manifold groups
• Subgroups of Surface Groups are Almost Geometric
• On L-spaces and left-orderable fundamental groups

Related

• On standard forms of 1--dominations between knots with same Gromov volumes
• Any 3-manifold 1-dominates at most finitely many geometric 3-manifolds
• Virtual domination of 3-manifolds II
• A note on the nearly additivity of knot width
• Natural properties of the trunk of a knot