Orbifold construction of the modes of the Poincare dodecahedral space

TL;DR

This paper introduces a novel method for constructing the modes of the Poincare dodecahedral space using orbifolds, Hopf maps, and Maxwell's multipole vectors, providing new geometric insights into their structure.

Contribution

It presents a new orbifold-based construction of the modes of the Poincare dodecahedral space, linking geometric and topological concepts to mode analysis.

Findings

The *235-orbifold acts as a parameter space for the modes.

The construction offers new geometric understanding of mode dimensions.

Provides explicit mode construction using orbifold techniques.

Abstract

We provide a new construction of the modes of the Poincare dodecahedral space S^3/I*. The construction uses the Hopf map, Maxwell's multipole vectors and orbifolds. In particular, the *235-orbifold serves as a parameter space for the modes of S^3/I* shedding new light on the geometrical significance of the dimension of each space of $k$-modes, as well as on the modes themselves.