Academy of Mathematics and Systems Science, CAS
Colloquia & Seminars

Speaker:	周嘉伟，北京雁栖湖应用数学研究院
Inviter:	黄瑞芝
Title:	The Formality of Sphere Bundles
Language:	Chinese
Time & Venue:	2023.12.20 14:30-15:30 南楼N802
Abstract:	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.