On the Obstructions to non-Cliffordian Pin Structures

TL;DR

This paper investigates the topological obstructions to non-Cliffordian pin structures on four-dimensional spacetimes, providing a general method applicable across dimensions and signatures, with implications for physics.

Contribution

It introduces a general framework for calculating obstructions to non-Cliffordian pin structures in various dimensions and signatures, and explores their physical significance.

Findings

Derived topological obstructions for non-Cliffordian pin structures

Presented a universal method applicable in any dimension and signature

Discussed the physical implications of pin structure breakdown

Abstract

We derive the topological obstructions to the existence of non-Cliffordian pin structures on four-dimensional spacetimes. We apply these obstructions to the study of non-Cliffordian pin-Lorentz cobordism. We note that our method of derivation applies equally well in any dimension and in any signature, and we present a general format for calculating obstructions in these situations. Finally, we interpret the breakdown of pin structure and discuss the relevance of this to aspects of physics.