MORSE INDEX OF A CYCLIC POLYGON. II

Abstract

A polygonal linkage can be imagined as a set of n rigid bars connected by links cyclically. This construction lies on a plane and can rotate freely around the links, with allowed self-intersections. On the moduli space of the polygonal linkage, the signed area function A is defined. G. Panina and G. Khimshiashvili proved that cyclic configurations of a polygonal linkage are the critical points of A. Later, G. Panina and the author described a way to compute the Morse index of a cyclic configuration of a polygonal linkage. In this paper a simple formula for the Morse index of a cyclic configuration is given. Also, a description is obtained for all possible local extrema of A.