Generalized Schönflies theorem

Geometry Topology Student Seminar
Wednesday, January 31, 2018 - 13:55
1 hour (actually 50 minutes)
Skiles 006
The Jordan curve theorem states that any simple closed curve decomposes the 2-sphere into two connected components and is their common boundary. Schönflies strengthened this result by showing that the closure of either connected component in the 2-sphere is a 2-cell. While the first statement is true in higher dimensions, the latter is not. However under the additional hypothesis of locally flatness, the closure of either connected component is an n-cell. This result is called the Generalized Schönflies theorem, and was proved independently by Morton Brown and Barry Mazur. In this talk, I will describe the proof of due to Morton Brown.