2025/02/27 by Ulrich Bauer, Bauer, Ulrich, Fabian Lenzen +1
Computer Science · Mathematics · #14-04 #57-08 #FOS: Mathematics #General Topology (math.GN) #Graph theory and applications #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2502.20149
openalex publication_date 2025/02/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The conformation space of cyclooctane, a ringlike organic molecule comprising eight carbon atoms, is a two-dimensional algebraic variety, which has been studied extensively for more than 90 years. We propose a cell structure representing this space, which arises naturally by partitioning the space into subsets of conformations that admit particular symmetries. We do so both for the labeled conformation space, in which the carbon atoms are considered as distinct, and for the actual, unlabeled, conformation space. The proposed cell structure is obtained by identifying subspaces of conformations based on symmetry patterns and studying the geometry and topology of these subsets using methods from dimensionality reduction and topological data analysis. Our findings suggest that, in contrast to the labeled variant, the conformation space of cyclooctane is contractible.