Forschungsseminar: Kirby Calculus

Abstract: In this seminar we are going to give a basic introduction to the notion of surgery on 3-manifolds and we will show how any closed, oriented, connected 3-manifold can be obtained from S^3 by doing surgery on a link. Then we will review some basic results of 4-manifold theory and learn about the Kirby moves. The goal is to finally give a sketch of the proof of Kirby's Theorem which states that two links are related by Kirby moves if and only if the manifolds obtained by surgery are homeomorphic.


References:

• W. B. Raymond Lickorish; An Introduction to Knot Theory; Springer 1997, 201 Seiten
  
• Nikolai Saveliev; Lectures on the Topology of 3-Manifolds:An Introduction to the Casson Invariant; Walter de Gruyter 1999, 199 Seiten
  
• R. Fenn and C. Rourke. On Kirby's calculus of links. Topology, 18(1):1-15, 1979.