# Spin-structures on real Bott manifolds with K\"ahler structures

## TL;DR

This paper characterizes when real Bott manifolds with Kähler structures admit Spin-structures, using cohomological techniques and Ishida's characterization, contributing to the understanding of their topological properties.

## Contribution

It provides necessary and sufficient conditions for the existence of Spin-structures on real Bott manifolds with Kähler structures, extending previous cohomological methods.

## Key findings

- Identifies conditions for Spin-structure existence
- Uses Ishida's characterization and cohomological techniques
- Builds on methods from Hantzsche-Wendt manifolds

## Abstract

Let M be a real Bott manifold with K\"{a}hler structure. Using Ishida characterization we give necessary and sufficient condition for the existence of the Spin-structure on M. In proof we use the technic developed in Popko, Szczepa\'{n}ski "Cohomological rigity of oriented Hantzsche-Wendt manifolds" (Adv. Math. 302 (2016), 1044 - 1068) and characteristic classes.