On the symplectic volume of the moduli space of Spherical and Euclidean polygons

Details On the symplectic volume of the moduli space of Spherical and Euclidean polygons On the symplectic volume of the moduli space of Spherical and Euclidean polygons

2005-07-14

arxiv.org/abs/math/0507281v1

Kodai Math. J. 28 (2005), no. 1, 199--208

Mathematics

Symplectic Geometry

Scientific paper

In this paper, we study the symplectic volume of the moduli space of polygons by using Witten's formula. We propose to use this volume as a measure for the flexibility of a polygon with fixed side-lengths. The main result of our is that among all the Spherical and Euclidean polygons with fixed perimeter the regular one is the most flexible and that among all the spherical polygons the regular one with side-length $\pi/2$ is the most flexible.

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