Speaker: 吕志教授，复旦大学

Inviter: 潘建中研究员

Title: Equivariant geometric bordism, representations and graphs

Language: Chinese

Time & Venue: 2024.06.19 16:00-17:00 N933

Abstract: Based upon a classical result of Conner and Floyd on involutions on manifolds, using the idea of the GKM theory, we show that an effective G-action on a smooth closed manifold fixing a finite set can always produce a G-labelled graph, on which all tangential G-representations at fixed points are equipped, where G is an elementary abelian 2-group. We further obtain a complete characterization of G-representations at fixed points of such an G-action in terms of its G-labelled graph, so that the ring generated by the equivariant geometric unoriented bordism classes of all such G-manifolds can be described in terms of G-labelled graphs. This enriches the GKM theory. In addition, we also obtain a complete characterization of G-representations at fixed points of such an G-action in terms of own way of G-representations. This is based on joint works with Bo Chen, Hao Li and Qiangbo Tan.