Introduction to geometric topology on 3-manifold
Lecturer
Yong Li (李镛, Assistant Professor, BIMSA)
Date
2025-09-17 ~ 2025-12-17
Schedule
Weekday Time Venue Online ID Password
Wed 17:05-18:40 A3-3-301 Zoom 442 374 5045 BIMSA
Wed 19:20-20:55 A3-3-301 Zoom 442 374 5045 BIMSA
Prerequisite
Elementary topology.
Introduction
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.
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
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)
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.
Video
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FROM 202.120.11.*