Graduate Student Colloquium

Leah Duffett, Department of Pure Mathematics, University of Waterloo

"Horned spheres and Schoenflies Theorem"

By the Generalized Jordon Curve Theorem, a topological 2-sphere S in R³ divides R³ in two: the exterior and interior of S. In 1924, J.W. Alexander gave examples of 2-spheres for which the exterior of S is not simply connected. I will present such an example and in doing so show that the Generalized Schoenflies Theorem does not hold for arbitrary topological spaces.

MC 4040