Cantor sets in \(S^ 3\) with simply connected complements
type: Item
instance of: scholarly article
title: Cantor sets in \(S^ 3\) with simply connected complements
zbMATH Open document ID: 0606.57006
DOI: 10.1016/0166-8641(86)90060-X
published in: Topology and its Applications
publication date: 1986-01-01T00:00:00Z
review text: The author gives a new example of a wild Cantor set in \(S^ 3\) with simply connected complement; it is ''defined by'' handlebodies of genus 2 and is simpler than the examples known previously. The author also gives two characterizations of tame Cantor sets: a Cantor set C in \(S^ 3\) is tame if and only if it satisfies at least one of the conditions: (a) every unknotted simple closed curve in \(S^ 3-C\) lies in the interior of a 3-disk in \(S^ 3-C\), (b) \(\pi_ 1(S^ 3-C-K)\) is finitely generated for each unknotted simple closed curve K in \(S^ 3-C\).
Mathematics Subject Classification ID: 57M30
Mathematics Subject Classification ID: 57N45
Mathematics Subject Classification ID: 57N30
Mathematics Subject Classification ID: 57M05
zbMATH DE Number: 3980030
zbMATH Keywords: wild Cantor set in \(S^ 3\) with simply connected complement
zbMATH Keywords: tame Cantor sets
author: Richard K. Skora
reviewed by: Joze Vrabec
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3980030