Introduction to geometric topology on 3-manifold
In this course, I will follow Part 3 of "An Introduction to Geometric Topology" by Martelli. I will try to explain the propositions in the book as clearly and thoroughly as possible, making this course very suitable for beginners. In the first few lectures, we will focus on the topological aspects of 3-manifolds, introducing some methods for constructing and decomposing them. Later, we will introduce metrics, with a particular focus on hyperbolic 3-manifolds.
讲师
日期
2025年09月17日 至 12月17日
位置
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| 周三 | 17:05 - 18:40 | A3-3-301 | Zoom 17 | 442 374 5045 | BIMSA |
| 周三 | 19:20 - 20:55 | A3-3-301 | Zoom 17 | 442 374 5045 | BIMSA |
修课要求
Elementary topology.
课程大纲
We will try to cover the 3rd part of Martelli's book:
1. Topology of three-manifolds
2. Seifert manifolds
3. Constructions of three-manifolds
4. The eight geometries
5. Mostow rigidity theorem
6. Hyperbolic three-manifolds
7. Hyperbolic Dehn filling
1. Topology of three-manifolds
2. Seifert manifolds
3. Constructions of three-manifolds
4. The eight geometries
5. Mostow rigidity theorem
6. Hyperbolic three-manifolds
7. Hyperbolic Dehn filling
参考资料
Bruno Martelli - An introduction to geometric topology, Part 3. (Book)
Nikolai Saveliev - Lectures on the topology of 3-manifolds: an introduction to the Casson invariant. (Book)
Allen Hatcher - Notes on basic 3-manifold topology. (Note, Hatcher’s homepage)
Nikolai Saveliev - Lectures on the topology of 3-manifolds: an introduction to the Casson invariant. (Book)
Allen Hatcher - Notes on basic 3-manifold topology. (Note, Hatcher’s homepage)
视频公开
公开
笔记公开
公开
语言
中文
, 英文
讲师介绍
During the course of his doctoral studies, Yong LI primarily focused on resurgence theory and its applications. His recent work involves exploring the application of resurgence theory to various subjects, including modular forms, topological invariants of 3-manifolds, quantum mechanics, etc.