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Introduction to 3-Manifolds
Last Updated: 2026-02-05 15:41:17
Abstract
This course provides an introduction to the basic notions and tools of geometric topology with a special focus on three dimensional manifolds.
Objective
In this course, we become familiar with the basic notions and tools of geometric topology, which concerns low-dimensional manifolds and their embeddings. We will focus on 3–dimensional manifolds. While this class of manifolds is very rich, it still allows for many structural results. An important goal of the lecture is to learn how to manipulate these manifolds: build them from simple pieces, cut them apart, isotope and simplify submanifolds etc. These techniques from differential topology are combined with invariants from algebraic topology, which are incredibly powerful in encoding properties of a 3–manifold. We discuss applications, which give new intuition for these invariants, and answer many questions about manifolds of dimension three or less. There are many synergies with Algebraic Topology II, which I encourage you to take in parallel.
Content
Background in differential topology Foundational results on the topology of 3–manifolds Knots and concordance
Resources
Literature
Knots and links by D. Rolfsen 3–Manifolds by J. Hempel Differential topology by T. Bröcker and K. Jänich
General Information
- Language
- English
- Levels
- MSC
Examination
- Type
- session examination
- Mode
- oral 30 minutes
Course Components
| Type | Title | Time & Place | Hours |
|---|---|---|---|
| lecture | Introduction to 3-Manifolds |
|
2 h weekly |
Offered In
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Electives (For the Master's degree in Applied Mathematics the following additional condition (not manifest in myStudies) must be obeyed: At least 15 of the required 28 credits from core courses and electives must be acquired in areas of applied mathematics and further application-oriented fields.)
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