Cantor sets in \(S^ 3\) with simply connected complements

DOI10.1016/0166-8641(86)90060-XzbMath0606.57006MaRDI QIDQ1084705

Richard K. Skora

Publication date: 1986

Published in: Topology and its Applications (Search for Journal in Brave)

zbMATH Keywords

tame Cantor setswild Cantor set in \(S^ 3\) with simply connected complement

Mathematics Subject Classification ID

Fundamental group, presentations, free differential calculus (57M05) Wild embeddings (57M30) Flatness and tameness of topological manifolds (57N45) Engulfing in topological manifolds (57N30)

Related Items

Rigid cantor sets in $R^3$ with simply connected complement ⋮ Simply connected 3-manifolds with a dense set of ends of specified genus ⋮ Simply connected open 3-manifolds with rigid genus one ends ⋮ Genus 2 Cantor sets ⋮ Cantor sets with high-dimensional projections ⋮ On defining sequences for Cantor sets ⋮ Engulfing and Finitely Generated Groups ⋮ Distinguishing Bing-Whitehead Cantor sets ⋮ Inequivalent Cantor sets in $R^{3}$ whose complements have the same fundamental group ⋮ A Cantor set with hyperbolic complement ⋮ Genus of a Cantor set

Cites Work

• Necessary and sufficient conditions that a 3-manifold be \(S^3\)
• Cantor sets in 3-manifolds
• Some wild cells and spheres in three-dimensional space
• Generalization of a construction of Antoine
• A homeomorphism between the 3-sphere and the sum of two solid horned spheres
• A wild Cantor set in $E^n$ with simply connected complement
• Three-Dimensional Manifolds with Finitely Generated Fundamental Groups
• Embedding Phenomena Based upon Decomposition Theory: Wild Cantor Sets Satisfying Strong Homogeneity Properties
• Decompositions of E 3 with a Compact O-Dimensional Set of Nondegenerate Elements
• Concerning Wild Cantor Sets in E 3
• Compact Submanifolds of 3-Manifolds
• Wild 0-dimensional sets and the fundamental group

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