Calculating Equivariant Homotopy Groups

Abstract

The study of algebraic invariants of topological spaces is an important part of topology. We find, for example, that the problem of distinguishing spaces from each other can often be answered by examining homotopy groupshomotopy groups, cohornology rings, and sometimes, as is the basis here, equivariant homotopy groups. In this paper, we demonstrate some calculations of equivariant homotopy groups. A few concepts from the study of topology are included with some detail, in particular definitions and examples of homotopy groups, equivariant maps, and equivariant homotopy groups. We then develop techniques for making calculations and present several interesting examples of equivariant homotopy groups.