Integral homology groups of double coverings and rank one $\mathbb{Z}$-local system for minimal CW complex

Ye Liu, Yongqiang Liu

Let $X$ be a connected finite CW complex. A connected double covering of $X$ is classified by a non-zero cohomology class $\omega \in H^1(X,{\mathbb{Z}}_2)$. Denote the double covering spa…