A criterion for the noncellularity of arcs
A wild Cantor set in with simply connected complement
A wildly embedded 1-dimensional compact set in each of whose components is tame
About neighborhoods of surfaces integrally unknotted in
Bing-Whitehead Cantor sets
Decomposition spaces having arbitrarily small neighborhoods with 2-sphere boundaries II
Decompositions of manifolds into codimension one submanifolds
Double suspension d'une sphère d'homologie
Group negative curvature for 3-manifolds with genuine laminations.
Homogeneity of dynamically defined wild knots.
In this paper we prove that a wild knot K which is the limit set of a Kleinian group acting conformally on the unit 3-sphere, with its standard metric, is homogeneous: given two points p, q ∈ K, there exists a homeomorphism f of the sphere such that f(K) = K and f(p) = q. We also show that if the wild knot is a fibered knot then we can choose an f which preserves the fibers.
Homogeneously wild curves and infinite knot products
Homotopy groups of arc complements in or Q
On the scarcity of tame disks in certain mild cells
On the simultaneous embedding of uncountably many distinct wild arcs with one wild endpoint in , a geometric approach
Open 3-manifolds, wild subsets of S3 and branched coverings.
In this paper, a representation of closed 3-manifolds as branched coverings of the 3-sphere, proved in [13], and showing a relationship between open 3-manifolds and wild knots and arcs will be illustrated by examples. It will be shown that there exist a 3-fold simple covering p : S3 --> S3 branched over the remarkable simple closed curve of Fox [4] (a wild knot). Moves are defined such that when applied to a branching set, the corresponding covering manifold remains unchanged, while the branching...
Representations of the Whitehead manifold and Julia sets
Representing open 3-manifolds as 3-fold branched coverings.
It is proved that the Freudenthal compactification of an open, connected, oriented 3-manifold is a 3-fold branched covering of S3, and in some cases, a 2-fold branched covering of S3. The branching set is a locally finite disjoint union of strings.
Rigid sets in manifolds
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...
Some New Invariants of Links.