The end-sum operation is a way of combining two manifolds of the same dimension. It is similar to the more familiar connected sum, but is less well-studied. The end-sum has been used primarily to create non-compact manifolds with specific properties. Surfaces are some of the simplest manifolds, and so it is natural to ask if one can describe the end-sum of surfaces.
In this talk, I will go over the construction of the end-sum. Then, I will describe the main properties of surfaces, and how they change during an end-sum.