2011/07/01 by Mikhail Khristoforov, Gaiane Panina, Khristoforov, Mikhail +1 · 2 citations
Biochemistry, Genetics and Molecular Biology · Computer Science · Mathematics · #51F99 #Computational Geometry and Mesh Generation #FOS: Mathematics #Genome Rearrangement Algorithms #Geometric and Algebraic Topology #Metric Geometry (math.MG) #math.MG #msc:51F99
paper · pdf · doi:10.48550/arxiv.1107.0126
openalex publication_date 2011/07/01 · arxiv created 2011/11/18 · arxiv updated 2011/11/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The basic object of the paper is the moduli space M2,3(L) of a closed polygonal linkage either in ℝ2 or in ℝ3. As was originally suggested by G. Khimshiashvili, the space M2(L) is equipped with the oriented area function A, whereas (as is suggested in the paper) M3(L) is equipped with the vector area function S. The latter are generically Morse functions, whose critical points have a nice description. In the preprint, we define a swap action (that is, the action of some group generated by edge transpositions) on the space M2,3(L) which preserves the functions A and S and the Morse points. We prove that the commutant of the group acts trivially, present some computer experiments and formulate a conjecture.