Klara Stokes: Rigidity and motion of articulated structures

Abstract.

The graphs that are minimally rigid when realised as bar and joint structures in the Euclidean plane are the so-called (2,3)-tight graphs. In three dimensions, no good combinatorial characterisation of the minimally rigid bar and joint structures is known. Cauchy's theorem in geometry says that if two convex polyhedra has congruent faces, then they are congruent. In general, determining the rigidity of geometric realisations of combinatorial objects is a difficult task. In this talk I will give an introduction to rigidity theory and then explain how to model many problems in rigidity theory using graphs of groups. If time permits I will also survey the use of geometric homology in rigidity theory.