Selection Rules for Topology Change
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...
Dans cet article nous étudions les singularités des applications différentiables de la deux sphère dans une trois variété avec les méthodes de transversalité et nous utilisons les résultats obtenus pour reprendre dans le cas différentiable, les démonstrations de Papakyriakopoulos et de Whitehead du théorème de la sphère.
We introduce a skeletal structure in , which is an - dimensional Whitney stratified set on which is defined a multivalued “radial vector field” . This is an extension of notion of the Blum medial axis of a region in with generic smooth boundary. For such a skeletal structure there is defined an “associated boundary” . We introduce geometric invariants of the radial vector field on and a “radial flow” from to . Together these allow us to provide sufficient numerical conditions for...