中科院数学与系统科学研究院

数学研究所

学术报告

拓扑研讨班

报告人：沈文 (首都师范大学)  

题  目：Topological classification of Bazaikin spaces

时  间：2023.09.20（星期三）14:30-16:30

地  点：数学院南楼N802

摘  要：Manifolds with positive sectional curvature have been a central object dates back to the beginning of Riemannian geometry. Up to homeomorphism, there are only finitely many examples of simply connected positively curved manifolds in all dimensions except in dimension 7 and 13, namely, Aloff-Wallach spaces and Eschenburg spaces in dimension 7, and the Bazaikin spaces in dimension 13. The topological classification modelled on the 7-dimensional examples has been carried out by Kreck-Stolz which leads to a complete solution for the Aloff-Wallach spaces. The main goal of this talk is the topological classification of 13-dimensional manifolds modelled on the Bazaikin spaces.