Rigidity with few locations

Karim Adiprasito; Eran Nevo

doi:10.1007/s11856-020-2076-y

Rigidity with few locations

Karim Adiprasito, Eran Nevo

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

Graphs triangulating the 2-sphere are generically rigid in 3-space, due to Gluck-Dehn-Alexandrov-Cauchy. We show there is a finite subset A in 3-space so that the vertices of each graph G as above can be mapped into A to make the resulted embedding of G infinitesimally rigid. This assertion extends to the triangulations of any fixed compact connected surface, where the upper bound obtained on the size of A increases with the genus. The assertion fails, namely no such finite A exists, for the larger family of all graphs that are generically rigid in 3-space and even in the plane.

Original language	English
Pages (from-to)	711-723
Number of pages	13
Journal	Israel Journal of Mathematics
Volume	240
Issue number	2
DOIs	https://doi.org/10.1007/s11856-020-2076-y
State	Published - 1 Oct 2020
Externally published	Yes

ASJC Scopus subject areas

General Mathematics

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title = "Rigidity with few locations",

abstract = "Graphs triangulating the 2-sphere are generically rigid in 3-space, due to Gluck-Dehn-Alexandrov-Cauchy. We show there is a finite subset A in 3-space so that the vertices of each graph G as above can be mapped into A to make the resulted embedding of G infinitesimally rigid. This assertion extends to the triangulations of any fixed compact connected surface, where the upper bound obtained on the size of A increases with the genus. The assertion fails, namely no such finite A exists, for the larger family of all graphs that are generically rigid in 3-space and even in the plane.",

author = "Karim Adiprasito and Eran Nevo",

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AU - Nevo, Eran

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AB - Graphs triangulating the 2-sphere are generically rigid in 3-space, due to Gluck-Dehn-Alexandrov-Cauchy. We show there is a finite subset A in 3-space so that the vertices of each graph G as above can be mapped into A to make the resulted embedding of G infinitesimally rigid. This assertion extends to the triangulations of any fixed compact connected surface, where the upper bound obtained on the size of A increases with the genus. The assertion fails, namely no such finite A exists, for the larger family of all graphs that are generically rigid in 3-space and even in the plane.

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ER -

Rigidity with few locations

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