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: 雷逢春教授（大连理工大学）
题 目: Some 3-manifold invariants derived from the intersecting kernels of Heegaard splittings
时 间: 2024.06.19(星期三) 15:00-16:00
地点：南楼933
摘 要:In the talk, I will desccribe some some quotient groups of the intersecting kernels of Heegaard splittings and show they are independent of the choice of the Heegaard splittings, therefore they are invariants of 3-manifolds M, in which the Reidmester-Singer Theorem on the stable equivalence of Heegaard splittings plays an essential role.
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报告人: 吕志教授（复旦大学）
题 目:Equivariant geometric bordism, representations and graphs
时 间: 2024.06.19(星期三) 16:00-17:00
地点：南楼933
摘 要: 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.
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