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arXiv 1902.092102019-02math.MG

The global rigidity of a framework is not an affine-invariant property

Victor Alexandrov

备注：: 7 pages, 4 figures. In version 2, the main result of this preprint is positioned more accurately with respect to the results of the predecessors

英文摘要：

It is well-known that the property of a bar-and-joint framework `to be infinitesimally rigid' is invariant under projective transformations of Eucliean $d$-space for every $d\geqslant 2$. It is less known that the property of a bar-and-joint framework `to be globally rigid' is not invariant even under affine transformations of the Euclidean plane. In this note, we prove of the latter statement for Euclidean $d$-space for every $d\geqslant 2$.

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