Mathematical Sciences: 4-Manifolds and Homology 3-Spheres

点击翻译按钮获取中文摘要

The main concern of this project is to study the role played by representations of the fundamental group of a homology 3- sphere on the 4-manifolds which it bounds. To this end the investigator plans to study new invariants of homology 3-spheres and their relationship with 4-dimensional topology. These invariants include Floer homology, the invariant "R" of the investigator and R. Stern, and a new invariant related to both of these. He hopes to be able to compute the Floer homology of all Seifert fibered homology spheres and to relate the results to the other invariants mentioned. These invariants should be useful tools. Furthermore, there is some reason to believe these techniques can be extended beyond the realm of Seifert fibrations.