Given a string  of npositive real numbers, one considers the moduli space  of closed spatial polygonal curves having edge lengths  The complex manifold  contains various complex hypersurfaces. We study the relationship between the homology classes represented by them. We also study the problem for the moduli space of planar polygonal curves. As an application, we study the following question: It is known that there is a diffeomorphism F between certain planar polygon spaces. We study how the homology classes correspond under F.

polygon space, homology class, hypersurface.