Inferring a Cell Structure on the Space of Cyclooctane Conformations

MCML Authors

Ulrich Bauer

Prof. Dr.

Core PI

Applied Topology and Geometry

Abstract

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.

inproceedings BL23

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MathSEE 2023

Symposium on Mathematics in Sciences, Engineering and Economics. Karslruhe, Germany, Sep 27-29, 2023.

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Authors

U. Bauer • F. Lenzen

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Links

DOI

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Research Area

 A2 | Mathematical Foundations