turkmath.org

In this talk we will discuss constructing topological spaces by gluing basic building blocks to each other. In a joint work with Aslı Güçlükan İlhan, we explain how such gluing data can be obtained from equivariant homotopy diagrams when certain obstructions vanish. Then we explain how the combinatorial nature of these constructions, determined by the gluing data, can be exploited to understand the homotopy types of these topological spaces. Given a finite group $G$, the main goal will be to construct finite $G-CW$-complexes homotopy equivalent to a product of spheres with isotropy groups in a given family of subgroups of $G$.