As a mathematical model for cycloalkenes, we consider equilateral polygons whose interior angles are the same except for those of the both ends of the specified edge. We study the configuration space of such polygons. It is known that when the polygons are almost regular, the configuration space is homeomorphic to S^n-4. In this paper, we prove that the configuration space is in fact diffeomorphic to the standard sphere S^n-4.

polygon space, interior angle, standard sphere, diffeomorphism.

Received: January 14, 2022; Accepted: February 24, 2022; Published: March 1, 2022

How to cite this article: Yasuhiko Kamiyama, The differential structure on the configuration space of a mathematical model for cycloalkenes, JP Journal of Geometry and Topology 27 (2022), 11-31. http://dx.doi.org/10.17654/0972415X22002

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

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