Shrinking of toroidal decomposition spaces

Daniel Kasprowski, and Mark Powell. "Shrinking of toroidal decomposition spaces." Fundamenta Mathematicae 227.3 (2014): 271-296. <http://eudml.org/doc/283034>.

@article{DanielKasprowski2014,
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.},
author = {Daniel Kasprowski, Mark Powell},
journal = {Fundamenta Mathematicae},
keywords = {decomposition space; Bing shrinking; Milnor invariants},
language = {eng},
number = {3},
pages = {271-296},
title = {Shrinking of toroidal decomposition spaces},
url = {http://eudml.org/doc/283034},
volume = {227},
year = {2014},
}

TY - JOUR
AU - Daniel Kasprowski
AU - Mark Powell
TI - Shrinking of toroidal decomposition spaces
JO - Fundamenta Mathematicae
PY - 2014
VL - 227
IS - 3
SP - 271
EP - 296
AB - 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.
LA - eng
KW - decomposition space; Bing shrinking; Milnor invariants
UR - http://eudml.org/doc/283034
ER -