turkmath.org

One can construct a topological space with a group action by gluing topological spaces with group actions to each other. Here the difficult part is to construct the correct gluing data so that the resulting space has the required properties. Our aim is to construct finite G-CW-complexes homotopy equivalent to a product of spheres with prescribed isotropy groups where G is a finite group. In this talk, we will explain how to obtain a gluing data for such a construction from equivariant homotopy diagrams when certain obstructions vanish. We also discuss how the combinatorial nature of the construction can be used to understand the homotopy type of the resulting space. This is a joint work with Özgün Ünlü.