Homogeneous $\mathbb Z/2$-Harmonic Forms and Spinors on $\mathbb{R}^4$ from Regular 4-Polytopes

TL;DR

This paper introduces new local singularity models for harmonic forms and spinors in four dimensions, based on homogeneous versions on 4 with singular sets derived from regular 4-polytopes.

Contribution

It presents novel homogeneous models for -harmonic forms and spinors in  with singularities related to regular 4-polytopes, expanding understanding of singularity structures.

Findings

Models are homogeneous on  with singular sets as cones on 1-skeleta of regular 4-polytopes.

Provides explicit descriptions of singularity models for harmonic forms and spinors.

Enhances the geometric understanding of singularities in gauge theory and harmonic analysis.

Abstract

We describe novel local singularity models for $\mathbb Z/2$ harmonic 1-forms, self-dual 2-forms and spinors in dimension 4. These models are homogeneous versions on $\mathbb{R}^4$ whose singular sets are cones on the 1-skeletal of certain regular 4-dimensional polytopes.