Shrinking of toroidal decomposition spaces

• Autorzy: Daniel Kasprowski , Mark Powell
• Języki publikacji: EN

Abstrakty

EN

Given a sequence of oriented links L¹,L²,L³,... each of which has a distinguished, unknotted component, there is a decomposition space 𝓓 of S³ naturally associated to it, which is constructed as the components of the intersection of an infinite sequence of nested solid tori. The Bing and Whitehead continua are simple, well known examples. We give a necessary and sufficient criterion to determine whether 𝓓 is shrinkable, generalising previous work of F. Ancel and M. Starbird and others. This criterion can effectively determine, in many cases, whether the quotient map S³ → S³/𝓓 can be approximated by homeomorphisms.

Kategorie tematyczne

• 57N12: Topology of E 3 and S 3
• 57M25: Knots and links in S 3
• 57M30: Wild knots and surfaces, etc., wild embeddings

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2014
• Tom: 227
• Numer: 3
• Strony: 271-296

Daty

wydano

2014

Twórcy

autor

Daniel Kasprowski

• Westfälische Universität Münster, Einsteinstrasse 62, 48149 Münster, Germany

autor

Mark Powell

• Department of Mathematics, Indiana University, Bloomington, IN 47405, U.S.A.
• Max Planck Institute for Mathematics, Vivatsgasse 7, 53111 Bonn, Germany

Identyfikatory

DOI

10.4064/fm227-3-3