Whitehead doubling, rank estimate and nonembeddability of contractible open manifolds

2025/10/08 by Shijie Gu, Jian Wang, Gu, Shijie +3
Mathematics · #FOS: Mathematics #General Topology (math.GN) #Geometric Analysis and Curvature Flows #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Geometry and complex manifolds #Group Theory (math.GR)

paper · pdf · doi:10.48550/arxiv.2510.06598

openalex publication_date 2025/10/08 · openalex created_date 2025/10/18 · openalex updated_date 2026/07/28

Abstract

Let K be a nontrivial knot. For each n∈ ℕ, we prove that the rank of its nth iterated Whitehead doubled knot group π₁(S³ ∖ WDⁿ(K)) is bounded below by n+1. As an application, we show that there exist infinitely many non-homeomorphic contractible open n-manifolds (n≥ 3) which cannot embed in a compact, locally connected and locally 1-connected n-dimensional metric space.

Citations

• Coxeter quotients of knot groups through 16 crossings
• Strong rigidity ofQ-rank 1 lattices

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