In [4], we determined the topological type of the configuration space of equilateral and equiangular heptagons for generic bond angle. In this paper, we determine the topological type of the configuration space of equilateral and equiangular octagons for the case when the bond angle θ satisfies

polygon space, bond angle, topological type.

Received: August 6, 2021; Accepted: September 8, 2021; Published: September 10, 2021

How to cite this article: Yasuhiko Kamiyama, The configuration space of equilateral and equiangular octagons, JP Journal of Geometry and Topology 26(2) (2021), 117-129. DOI: 10.17654/GT026020117

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

References:

[1] G. M. Crippen, Exploring the conformation space of cycloalkanes by linearized embedding, J. Comput. Chem. 13 (1992), 351-361.
[2] M. Farber, Invitation to topological robotics, Zurich Lectures in Advanced Mathematics, European Mathematical Society (EMS), 2008.
[3] Y. Kamiyama, A filtration of the configuration space of spatial polygons, Adv. Appl. Discrete Math. 22(1) (2019), 67-74.
[4] Y. Kamiyama, The configuration space of equilateral and equiangular heptagons, JP J. Geom. Topol. 25(1-2) (2020), 25-33.
[5] Y. Kamiyama, On the singularity of the configuration space of equilateral and equiangular polygons, Advances and Applications in Discrete Mathematics (submitted).
[6] M. Kapovich and J. Millson, The symplectic geometry of polygons in the Euclidean space, J. Differential Geom. 44 (1996), 479-513.
[7] J. O’Hara, The configuration space of equilateral and equiangular hexagons, Osaka J. Math. 50 (2013), 477-489.