Matthias Nagel: Catalogue data in Spring Semester 2020 |
Name | Dr. Matthias Nagel |
URL | https://nagel.io |
Department | Mathematics |
Relationship | Lecturer |
Number | Title | ECTS | Hours | Lecturers | |
---|---|---|---|---|---|
401-4532-20L | Introduction to 3-Manifolds | 4 credits | 2V | M. Nagel | |
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 | ||||
Literature | Knots and links by D. Rolfsen 3–Manifolds by J. Hempel Differential topology by T. Bröcker and K. Jänich | ||||
Prerequisites / Notice | Algebraic Topology I Differential Geometry I |