Shin-ichi Tanigawa: Global rigidity of triangulated manifolds

EGERVÁRY SZEMINÁRIUM

Abstract:
The rigidity of triangulated surfaces is a classical topic
in discrete geometry. In this work, we prove that if G is the graph of
a triangulated (d-1)-manifold for d \geq 3, then G is generically
globally rigid in R^d if and only if it is (d+1)-connected and, if d =
3, G is not planar. The special case d = 3 resolves a conjecture of
Connelly. We also give applications to the lower bound theorem and the
reconstruction problem of convex polytopes.
This talk is based on joint work with James Cruickshank and Bill Jackson.