# Generic Global Rigidity in Complex and Pseudo-Euclidean Spaces

 Title: Generic Global Rigidity in Complex and Pseudo-Euclidean Spaces Author: Gortler, Steven J.; Thurston, Dylan P. Note: Order does not necessarily reflect citation order of authors. Citation: Gortler, Steven J. and Dylan P. Thurston. 2014. Generic global rigidity in complex and pseudo-Euclidean spaces. The Fields Institute Conference Proceedings 2014. Full Text & Related Files: gortler_0.pdf (367.0Kb; PDF) Abstract: In this paper we study the property of generic global rigidity for frameworks of graphs embedded in d-dimensional complex space and in a d-dimensional pseudo-Euclidean space R$$^{2}$$ with a metric of indefinite signature). We show that a graph is generically globally rigid in Euclidean space iff it is generically globally rigid in a complex or pseudo-Euclidean space. We also establish that global rigidity is always a generic property of a graph in complex space, and give a sufficient condition for it to be a generic property in a pseudo-Euclidean space. Extensions to hyperbolic space are also discussed. Other Sources: http://arxiv.org/abs/1212.6685 Terms of Use: This article is made available under the terms and conditions applicable to Open Access Policy Articles, as set forth at http://nrs.harvard.edu/urn-3:HUL.InstRepos:dash.current.terms-of-use#OAP Citable link to this page: http://nrs.harvard.edu/urn-3:HUL.InstRepos:11856176 Downloads of this work: