Geodesic
The Euler characteristic of the regular spherical polygon spaces
Homology, homotopy, and applications, Tome 22 (2020) no. 1, pp. 1-10.

Voir la notice de l'article provenant de la source International Press of Boston

Let $a$ be a real number satisfying $0 \lt a \lt \pi$. We denote by $M_n (a)$ the configuration space of regular spherical $n$-gons with side-lengths $a$. The purpose of this paper is to determine $\chi (M_n (a))$ for all a and odd $n$. To do so, we construct a manifold $X_n$ and a function $\mu : X_n \to \mathbb{R}$ such that $\mu^{-1} (a) = M_n (a)$. In fact, the function μ is different from the Kapovich–Millson Morse function. We determine the index of each critical point of $\mu$. Since a level set is obtained by successive Morse surgeries, we can determine $\chi (M_n (a))$.
DOI : 10.4310/HHA.2020.v22.n1.a1
Classification : 58D29, 58E05
Keywords: spherical polygon space, Morse function, Euler characteristic 
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Yasuhiko Kamiyama. The Euler characteristic of the regular spherical polygon spaces. Homology, homotopy, and applications, Tome 22 (2020) no. 1, pp. 1-10. doi : 10.4310/HHA.2020.v22.n1.a1. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2020.v22.n1.a1/

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