We impose conditions on the bond angles of an equilateral pentagon in R³. Assuming that the first and last bond angles are θ, we define the configuration space X₅(θ). On the other hand, assuming that the first and fourth bond angles are θ, we define the configuration space Y₅(θ). We study whether X₅(θ) and Y₅(θ) are homeomorphic.

polygon space; pentagon; bond angle.

Received: October 27, 2023;  Accepted: November 21, 2023; Published: December 5, 2023

How to cite this article: Yasuhiko Kamiyama, The topology of subspaces of the configuration space of spatial pentagons, JP Journal of Geometry and Topology 29(2) (2023), 173-185. http://dx.doi.org/10.17654/0972415X23009

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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] S. Goto, K. Komatsu and J. Yagi, The configuration space of a model for ringed hydrocarbon molecules, Hiroshima Math. J. 42 (2012), 115-126.
[4] Y. Kamiyama, The topological type of equilateral and almost equiangular polygon spaces, J. Math. (2019), p. 6. Art. ID 6958218.
[5] Y. Kamiyama, The topology of the configuration space of a mathematical model for cycloalkenes, Advanced Topics of Topology, Intech. Open, London, 2022. https://www.intechopen.com/chapters/79299.
[6] M. Kapovich and J. Millson, The symplectic geometry of polygons in 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.