The rigidity of periodic frameworks as graphs on a fixed torus

Abstract

We define periodic frameworks as graphs on the torus, using the language of gain graphs. We present some fundamental definitions and results about the infinitesimal rigidity of graphs on a torus of fixed size and shape, and find necessary conditions for the generic rigidity of pe- riodic frameworks on a d-dimensional fixed torus.

arXiv comment42 pages, 9 figures