University of Birmingham > Talks@bham > Study group in Graph Theory, Topology and Algorithms > Rigidity of symmetry-forced frameworks

Rigidity of symmetry-forced frameworks

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If you have a question about this talk, please contact Johannes Carmesin.

The fundamental problem in rigidity theory is to determine whether a given immersion of a graph into d-dimensional eucledian space R(d) can be continuously deformed, treating the edges as rigid struts that can move freely about their incident vertices. For a fixed graph G, either all generic immersions of G into R(d) are rigid, in which case we say that G is generically rigid in R(d), or all generic immerisions of G into R(d) are not rigid, in which case we say that G is generically flexible in R(d). Perhaps the most well-known result in this area is Laman’s theorem, which is a combinatorial characterization of the graphs that are generically minimally rigid in the place R(2). In applications to crystallography, the relevant frameworks have symmetry that continuous deformations must preserve. The main result of this talk is a Laman-like theorem for symmetric frameworks with certain kinds of symmetry.

This talk is part of the Study group in Graph Theory, Topology and Algorithms series.

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