Around a conjecture by R. Connelly, E. Demaine, and G. Rote

2011/06/06 by Alexander Igamberdiev, Gaiane Panina, Igamberdiev, Alexander +1
Computer Science · Engineering · Mathematics · #55M99 #Advanced Materials and Mechanics #Algebraic Topology (math.AT) #Computational Geometry and Mesh Generation #FOS: Mathematics #Structural Analysis and Optimization #math.AT #msc:55M99

paper · pdf · doi:10.48550/arxiv.1106.1134

openalex publication_date 2011/06/06 · arxiv created 2011/06/13 · arxiv updated 2011/06/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Denote by M(P) the configuration space of a planar polygonal linkage, that is, the space of all possible planar configurations modulo congruences, including configurations with self-intersections. A particular interest attracts its subset M^o(P) ⊂ M(P) of all configurations without self-intersections. R. Connelly, E. Demaine, and G. Rote proved that M^o(P) is contractible and conjectured that so is its closure M^o(P). We disprove this conjecture by showing that a special choice of P makes the homologies H_k(M^o(P)) non-trivial.

Related

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