A numerous number of closed simply connected Sasaki-Einstein manifolds, in particular 5-manifolds, have been found based on the method introduced by Shoshichi Kobayashi, and developed by Charles Boyer, Krzysztof Galicki, and János Kollár. In this talk, we briefly explain how to find closed simply connected 5-manifolds that allow Sasaki-Einstein metrics. By using methods in K-stability, we newly verify that several closed simply connected 5-manifolds allow Sasaki-Einstein structures. We then list closed simply connected 5-manifolds that are known so far to admit Sasaki-Einstein structures.
This video was produced by the Japan-US Mathematics Institute and forms part of JAMI Conference 2022.
