Spin structures on flat manifolds

TL;DR

This paper introduces an algorithmic method to determine the existence of spin structures on flat manifolds, with applications demonstrated in 5- and 6-dimensional cases.

Contribution

It provides a novel algorithmic approach for analyzing spin structures specifically on flat manifolds in higher dimensions.

Findings

Successfully applied to 5-dimensional flat manifolds

Successfully applied to 6-dimensional flat manifolds

Advances understanding of spin structures in higher dimensions

Abstract

We present an algorithmic approach to the problem of existence of spin structures on flat manifolds. We apply our method in the cases of flat manifolds of dimensions 5 and 6.