On embedding infinite cyclic covers in compact 3-manifolds

2006/08/14 by C. McA. Gordon, Gordon, C. McA.
Mathematics · #57M25 #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology

paper · pdf · doi:10.48550/arxiv.math/0608339

openalex publication_date 2006/08/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that the infinite cyclic cover of the exterior of the untwisted Whitehead double of a non-trivial knot does not embed in any compact 3-manifold, answering a question of Jiang, Ni, Wang and Zhou.

Related

• Embedding infinite cyclic covers of knot spaces into 3-space
• On the cyclic 3-manifold covers of the type surface x R
• On the determination of knots by their cyclic unbranched coverings
• Torsion in the homology of finite covers of 3-manifolds
• Cyclic branched covers of alternating knots