Spin-structures on real Bott manifolds with K\"{a}hler structure

TL;DR

This paper provides a complete characterization of when real Bott manifolds with Kähler structures admit spin-structures, using Ishida's criteria, characteristic classes, and advanced techniques.

Contribution

It offers the first necessary and sufficient conditions for the existence of spin-structures on these manifolds, expanding understanding of their geometric and topological properties.

Findings

Derived explicit criteria for spin-structure existence

Applied Ishida's characterization to real Bott manifolds

Utilized characteristic classes and advanced techniques

Abstract

Let $M$ be a real Bott manifold with K\"{a}hler structure. Using Ishida characterization \cite{I11} we give necessary and sufficient condition for the existence of the spin-structure on $M$. In proof we use the technic developed in \cite{PS16} and characteristic classes.