Shrinking of toroidal decomposition spaces
Shrinking of toroidal decomposition spaces
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.
Bing shrinking, Decomposition space, Milnor invariants
271-296
Kasprowski, Daniel
44af11b9-4d22-49f2-a6a3-04009f45b075
Powell, Mark
4aaeb063-734c-4136-9da8-fb2ade23d744
2014
Kasprowski, Daniel
44af11b9-4d22-49f2-a6a3-04009f45b075
Powell, Mark
4aaeb063-734c-4136-9da8-fb2ade23d744
Kasprowski, Daniel and Powell, Mark
(2014)
Shrinking of toroidal decomposition spaces.
Fundamenta Mathematicae, 227 (3), .
(doi:10.4064/fm227-3-3).
Abstract
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.
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Published date: 2014
Keywords:
Bing shrinking, Decomposition space, Milnor invariants
Identifiers
Local EPrints ID: 478530
URI: http://eprints.soton.ac.uk/id/eprint/478530
ISSN: 0016-2736
PURE UUID: 8ff7daac-0023-4680-83c8-28e009e4f8db
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Date deposited: 04 Jul 2023 17:48
Last modified: 17 Mar 2024 04:19
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Author:
Daniel Kasprowski
Author:
Mark Powell
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