2022/07/17 by Blanc, David, Shvalb, Nir · 1 citation
#70B15 #Algebraic Topology (math.AT) #FOS: Mathematics #Primary 70G40 #Secondary 57R45
paper · doi:10.48550/arxiv.2207.08173
A configuration of a linkage Γ is a possible positioning of Γ in ℝd and the collection of all such forms the configuration space C(Γ) of Γ. We here introduce the notion of the symmetric configuration space of a linkage, in which we identify configurations which are geometrically indistinguishable. We show that the symmetric configuration space of a planar polygon has a regular cell structure, provide some principles for calculating this structure, and give a complete description of the symmetric configuration space of all quadrilaterals and of the equilateral pentagon.