Minimal Cell Structures for G-CW Complexes

In this paper, we consider the minimal cell structure problem forGCW complexes. A CW complex is a nice approximation of general topological spaces, which is constructed by repeating attaching higher dimensional cells to lower ones. A G-CW complex is its generalized version to spaces with a group action. The structure theorem for ordinary CW complexes is well-studied, and we can know the minimal number of cells needed to describe the topology properties of a space completely. However, when the group action is involved, the structure becomes much more complicated. In this paper, we set up an algebraic model for G-CW complexes and simplify the minimal cell structure problem a lot. We also successfully get the minimal structure in the simple case G = Z/pZ.