Group Theory and Modern Dance Composition

TL;DR

This paper explores the mathematical structure of spatial reference systems in dance, using group theory to formalize choreographic concepts like inversion and transposition, and introduces new devices based on polyhedral symmetries.

Contribution

It formalizes Laban Movement Analysis concepts as group homomorphisms and develops new choreographic devices using polyhedral group actions.

Findings

Inversion and transposition are shown to be group homomorphisms in LMA.

Mathematical definitions of orbits and stabilizers are applied to dance movements.

New choreographic devices are proposed based on polyhedral symmetries.

Abstract

This paper will examine the spatial reference systems typically used in Laban Movement Analysis (LMA), and the consequences of group actions on these systems. The elementary notions of inversion and transposition in choreographic composition can be defined in such a way that they can be shown to be group homomorphisms in all the reference systems of LMA. The notions of orbits and stabilizers on polyhedra are used to mathematically define these choreographic devices, and these same notions can be used to define new choreographic devices on the standard polyhedra used for spatial reference in dance.