Shrinking of toroidal decomposition spaces

Kasprowski, Daniel; Powell, Mark

doi:10.4064/fm227-3-3

Shrinking of toroidal decomposition spaces

Kasprowski, Daniel; Powell, Mark

Authors

Daniel Kasprowski

Mark Powell

Abstract

Given a sequence of oriented links L^1,L^2,L^3,... each of which has a distinguished, unknotted component, there is a decomposition of the 3-sphere 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 such a decomposition 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 which identifies the elements of the decomposition to points can be approximated by homeomorphisms.

Citation

Kasprowski, D., & Powell, M. (2014). Shrinking of toroidal decomposition spaces. Fundamenta Mathematicae, 227(3), 271-296. https://doi.org/10.4064/fm227-3-3

Journal Article Type	Article
Online Publication Date	Oct 8, 2014
Publication Date	Oct 8, 2014
Deposit Date	Oct 3, 2017
Publicly Available Date	Oct 4, 2017
Journal	Fundamenta Mathematicae
Print ISSN	0016-2736
Electronic ISSN	1730-6329
Publisher	Instytut Matematyczny
Peer Reviewed	Peer Reviewed
Volume	227
Issue	3
Pages	271-296
DOI	https://doi.org/10.4064/fm227-3-3
Related Public URLs	https://arxiv.org/abs/1307.0154