Gage Cosgrove

In a group, we may use a normal subgroup to form a quotient that is also agroup, the elements of which are the equivalence classes. Can we use agroup to form equivalence classes on a manifold to produce a manifold?We choose a group,G, a manifoldM, and a pointponM. We see whichpoints can be arrived at fromp(this is called the orbit ofpunderG). In thistalk, we explore specific group actions on particular manifolds and try todetermine what the orbit spaces are. We define what it means for a set to bea differentiable manifold and we introduce the Quotient ManifoldTheorem, which gives sufficient conditions for the orbit space to be adifferentiable manifold. A good understanding of linear algebra andcalculus are required. A knowledge of topology may help with thetechnical parts of the talk.