Note about Stiefel-Whitney classes on real Bott manifolds

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. Gąsior "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. Gąsior, A. Szczepański "Flat manifolds with holonomy group $Z_2^k$ of diagonal type" (Osaka J. Math. {\bf 51} (2014), 1015 - 1025).

Author is supported by the Polish National Science Center grant DEC-2017/01/X/ST1/00062