$\mathbb{Z}_k$-stratifolds

Abstract

Generalizing the ideas of $\mathbb{Z}_k$-manifolds from Sullivan and the theory of stratifolds from Kreck, we define $\mathbb{Z}_k$-stratifolds. We introduce the bordism theory of $\mathbb{Z}_k$-stratifolds in order to represent every homology class with $\mathbb{Z}_k$-coefficients. We present a geometric interpretation of the Bockstein long exact sequence and the Atiyah-Hirzebruch spectral sequence for $\mathbb{Z}_k$-bordism ($k$ odd)