2:00 pm Monday, December 2, 2019
Junior Topology: An application of Freedman's work by Kai Nakamura in RLM 12.166
With Freedman in town this week, I'll start off by taking a few minutes to discuss Freedman's work which showed that Casson handles are homeomorphic to standard 2-handles. This has many important corollaries, including the classification of topological 4-manifolds, the 4-dimensional Poincare conjecture, and the existence of exotic R^4's. We will then with our remaining time put a Stein structure on a Casson handle in a way that will allow us to control the genus of embedded surfaces on open 4-manifolds. For the sake of concreteness we will focus on how to attach a Casson handle to a legendrian unknot to get exotic R^2 x S^2 with control of the genus of surfaces that represent the homology class [pt x S^2]. With time permitting, we will try to illustrate how to use this idea to find exotic smooth structures on every open 2-handlebody. Submitted by
|
|