Twistors: Bridges among 3-manifolds
A simple configuration on bipartite 3-gems, named twistor is investigated. A twistor can be twisted in two different ways yielding two other twistors and proving simple moves internal to the class of 3-gems. The author proves this fact by recoupling twistors and by 1- and 2-dipole bridges among all orientable 3-manifolds. There is an important connection (not treated here) between this result on these combinatorial twists and the basic theorem of Lickorish that the 3-sphere can be reached from any 3-manifold by removing a finite number of disjoint solid tori and pasting them back differently. This connection will be algorithmically explored elsewhere.
scientific article; zbMATH DE number 1110112
scientific article