Nicholas Vlamis (Queens College), Topological ends and the classification of surfaces

The classification of compact surfaces is a foundational result in topology dating back to the late 18th- and early 19th-century. Though much less known, there is a classification of all second-countable surfaces, which relies on the theory of ends. In this talk, I will discuss the notion of a topological end and go over the classification of all surfaces due to Kerékjártó and Richards. This talk is motivated by the recent interest in studying homeomorphisms of non-compact surfaces, where this classification is essential.