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Junior Topology
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Kai Nakamura, RLM 12.166: An application of Freedman\'s work
Monday, December 02, 2019, 02:00pm - 03:00pm
With Freedman in town this week, I'll start off by taking a fewminutes to discuss Freedman's work which showed that Casson handlesare homeomorphic to standard 2-handles. This has many importantcorollaries, including the classification of topological 4-manifolds,the 4-dimensional Poincare conjecture, and the existence of exoticR^4's. We will then with our remaining time put a Stein structureon a Casson handle in a way that will allow us to control thegenus of embedded surfaces on open 4-manifolds. For the sakeof concreteness we will focus on how to attach a Casson handleto a legendrian unknot to get exotic R^2 x S^2 with control ofthe genus of surfaces that represent the homology class [pt xS^2]. With time permitting, we will try to illustrate how touse this idea to find exotic smooth structures on every open2-handlebody.
Location: RLM 12.166

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