Universal symmetries: Global equivariant homotopy theory

Abstract

Global equivariant homotopy theory is, informally speaking, the universal home for deformations of geometric structures with symmetry groups that vary coherently. It studies geometric and topological objects on which all compact Lie groups act at once and in a compatible and coherent way. In this survey article, we give a brief introduction to the subject with emphasis on recent applications to equivariant bordism.