On the classification and bifurcation of multigerms of maps from surfaces to 3-space

The Script A sign-classification of multigerm singularities is discussed, based on the theory of complete transversals. An Script A sign-classification of r-multigerms from the plane to 3-space of Script A sign-codimension < 6 - r is carried out and the bifurcation geometry of these singularities analysed. This work has applications to the study of two-dimensional spatial motions, giving local models for the singularities which appear on general trajectories of rigid body motions from the plane to 3-space. In addition, our classification is extensive enough to give the full list of simple multigerm singularities from the plane to 3-space.