Anthony Nixon

Global rigidity of linearly constrained frameworks

A bar-joint framework (G,p) in d-dimensional Euclidean space is the combination of a graph G and a map p assigning positions to the vertices of G. The framework is rigid if the only edge-length-preserving continuous motions of the vertices arise from isometries of d-space. The framework is globally rigid if every other framework with the same edge lengths arises from isometries of d-space. I will survey some important results about rigid and globally rigid frameworks and then introduce linearly constrained frameworks. Linearly constrained frameworks are a generalisation of frameworks in which some vertices are constrained to lie on one or more given hyperplanes. Streinu and Theran characterised rigid linearly constrained generic frameworks in 2-space in 2010. I will describe an analogous result for the global rigidity of linearly constrained generic frameworks in 2-space. If there is time I will also discuss extensions of these results for rigidity and global rigidity to higher dimensions.

This is joint work with Hakan Guler and Bill Jackson.