拓扑研讨班：The Formality of Sphere Bundles

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：周嘉伟（北京雁栖湖应用数学研究院）

题  目：The Formality of Sphere Bundles

时  间：2023.12.20（星期三）14:30-15:30

地  点：数学院南楼N802

摘  要：A manifold is called formal when it shares the same rational homotopy type as its cohomology ring. We first study the formality of a sphere bundle over a formal manifold. In this case the formality can be totally determined by the Bianchi-Massey tensor, a 4-tensor on a subspace of the cohomology ring, initially introduced by Crowley and Nordstrom. As a special case, we observe that if a manifold and its unit tangent bundle are both formal, then the manifold has either a zero Euler characteristic or a rational cohomology ring generated by one element. Lastly, we delve into the scenario of a general base manifold, presenting an obstruction of formality.