Note about Stiefel-Whitney classes on real Bott manifolds

TL;DR

This paper develops methods to compute even Stiefel-Whitney classes on real Bott manifolds, extending previous work on spin-structures and flat manifolds with holonomy group ^k.

Contribution

It provides a systematic approach to calculate all Stiefel-Whitney classes for real Bott manifolds, answering open questions and extending prior results.

Findings

Explicit formulas for even Stiefel-Whitney classes derived

Extended Ga5sior's work on spin-structures to all Stiefel-Whitney classes

Connected results to flat manifolds with diagonal holonomy groups

Abstract

Real Bott manifolds is a class of flat manifolds with holonomy group $\mathbb Z_2^k$ of diagonal type. In this paper we want to show how we can compute even Stiefel - Whitney classes on real Bott manifolds. This paper is an answer to the question of professor Masuda if is it possible to extend A. G\k{a}sior "Spin-structures on real Bott manifolds" (J. Korean Math. Soc. {\bf 54}, (2017), no. 2, 507 - 516) and compute any Stiefel-Whitney classes for real Bott manifolds. It also extends results of A. G\k{a}sior, A. Szczepa\'nski "Flat manifolds with holonomy group $Z_2^k$ of diagonal type" (Osaka J. Math. {\bf 51} (2014), 1015 - 1025).