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.
Lecturer
Date
17th September ~ 17th December, 2025
Location
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| Wednesday | 17:05 - 18:40 | A3-3-301 | Zoom 17 | 442 374 5045 | BIMSA |
| Wednesday | 19:20 - 20:55 | A3-3-301 | Zoom 17 | 442 374 5045 | BIMSA |
Prerequisite
Elementary topology.
Syllabus
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
Reference
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)
Video Public
Yes
Notes Public
Yes
Language
Chinese
, English
Lecturer Intro
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.