1998/10/20 by Henry C. King, King, Henry C. · 1 citation
Mathematics · #14P10 #57R99 #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #math.AG #math.GT #msc:14P10 #msc:57R99
paper · pdf · doi:10.48550/arxiv.math/9810130
6 figures
arxiv created 1998/10/20 · openalex publication_date 1998/10/20 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper characterizes which subsets of Cn can be the set of positions of n points on a linkage in the complex plane C. For example, assuming compactness they are just compact semialgebraic sets. Noncompact configuration spaces are semialgebraics sets invariant under the Euclidean group, with compact quotient.