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1. CJM 1998 (vol 50 pp. 581)

Kamiyama, Yasuhiko
The homology of singular polygon spaces
Let $M_n$ be the variety of spatial polygons $P= (a_1, a_2, \dots, a_n)$ whose sides are vectors $a_i \in \text{\bf R}^3$ of length $\vert a_i \vert=1 \; (1 \leq i \leq n),$ up to motion in $\text{\bf R}^3.$ It is known that for odd $n$, $M_n$ is a smooth manifold, while for even $n$, $M_n$ has cone-like singular points. For odd $n$, the rational homology of $M_n$ was determined by Kirwan and Klyachko [6], [9]. The purpose of this paper is to determine the rational homology of $M_n$ for even $n$. For even $n$, let ${\tilde M}_n$ be the manifold obtained from $M_n$ by the resolution of the singularities. Then we also determine the integral homology of ${\tilde M}_n$.

Keywords:singular polygon space, homology
Categories:14D20, 57N65

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