2003/06/30 by Michael Holcomb, Holcomb, Michael
Computer Science · Engineering · Mathematics · #55R70 #57N99 #Advanced Numerical Analysis Techniques #Algebraic Topology (math.AT) #Computational Geometry and Mesh Generation #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #math.AT #math.GT #msc:55R70 #msc:57N99
paper · pdf · doi:10.48550/arxiv.math/0307001
29 pages, 12 figures
arxiv created 2003/06/30 · openalex publication_date 2003/06/30 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The geometric, topological, and symplectic properties of moduli spaces (spaces of configurations modulo rotations and translations) of polygonal linkages have been studied by Kapovich, Millson, and Kamiyama, et. al. One can form a polygonal linkage by taking two free linkages and identifying initial and terminal vertices. This can be generalized so that one takes three free linkages and identifies initial and terminal vertices. Then one obtains a linkage which contains multiple polygons, any two of which have shared edges. The geometric and topological properties of moduli spaces of these multipolygonal linkages are studied. These spaces turn out to be compact algebraic varieties. Some conditions under which these spaces are smooth manifolds, cross products or disjoint unions of moduli spaces of polygonal linkages, or connected, are determined. In addition, dimensions in the smooth manifold cases and some Euler characteristics are computed.