Morse index of a cyclic polygon

TL;DR

This paper provides an explicit formula for the Morse index of the signed area function at cyclic configurations of planar polygonal linkages, linking combinatorial and metric properties.

Contribution

It introduces a new explicit formula for the Morse index of cyclic polygon configurations, incorporating both combinatorial and metric data.

Findings

Explicit Morse index formula for cyclic configurations

Dependence on combinatorial and metric properties

Advances understanding of critical points in polygonal linkages

Abstract

It is known that cyclic configurations of a planar polygonal linkage are critical points of the signed area function. In the paper, we announce an explicit formula of the Morse index for the signed area of a cyclic configuration. It depends not only on the combinatorics of a cyclic configuration, but also includes some metric characterization.