Kodai Mathematical Journal

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

Vu The Khoi

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Abstract

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 polygons with fixed perimeter in S3 or E3 the regular one is the most flexible and that among all the spherical polygons the regular one with side-length π/2 is the most flexible.

Article information

Source
Kodai Math. J., Volume 28, Number 1 (2005), 199-208.

Dates
First available in Project Euclid: 23 March 2005

Permanent link to this document
https://projecteuclid.org/euclid.kmj/1111588046

Digital Object Identifier
doi:10.2996/kmj/1111588046

Mathematical Reviews number (MathSciNet)
MR2122200

Zentralblatt MATH identifier
1104.53083

Citation

Khoi, Vu The. On the symplectic volume of the moduli space of spherical and Euclidean polygons. Kodai Math. J. 28 (2005), no. 1, 199--208. doi:10.2996/kmj/1111588046. https://projecteuclid.org/euclid.kmj/1111588046


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