Book Review: Combinatorial rigidity

Combinatorial Rigidity for Unicritical Polynomials

We prove that any unicritical polynomial fc : z 7→ z+c which is at most finitely renormalizable and has only repelling periodic points is combinatorially rigid. It implies that the connectedness locus (the “Multibrot set”) is locally connected at the corresponding parameter values. It generalizes Yoccoz’s Theorem for quadratics to the higher degree case. Stony Brook IMS Preprint #2005/05 July 2005

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Combinatorial and Algorithmic Volume Rigidity

We study the generic rigidity properties of systems of volume constraints. We formally define, in an algebraic geometrical setting, the volume rigidity problem and extract its underlying sparse hypergraph structure. Then we develop a combinatorial theory of cocircuit matroids which leads to a very general linear representation result for sparse hypergraphs. Applying this to the volume rigidity ...

Book Review

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