Topology

Catalog description

This course is a basic introduction to topology, with a balance between point-set topology, geometric topology, and algebraic topology. The concept of a topological space is introduced and some of its more important properties, like connectedness and compactness, are studied. Then the main focus is on topological surfaces with the aim of establishing the fundamental classification theorem for compact surfaces, connecting to the Euler characteristic. After developing the foundations and the geometric intuition, computational algebraic aspects such as homology are introduced. Further classification uses homotopy, the fundamental group, and covering spaces. The concepts are illustrated in various applications, including the Brouwer Fixed Point Theorem.