The rigidity of periodic frameworks as graphs on a fixed torus

Details The rigidity of periodic frameworks as graphs on a fixed torus The rigidity of periodic frameworks as graphs on a fixed torus

2012-02-29

arxiv.org/abs/1202.6652v1

Mathematics

Metric Geometry

42 pages, 9 figures

Scientific paper

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.

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