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
Performance assessment
Performance assessment information (valid until the course unit is held again)
The performance assessment is offered every session. Repetition possible without re-enrolling for the course unit.
Mode of examination
oral 30 minutes
Additional information on mode of examination
BITTE BEACHTEN: Die mündliche Prüfung dauert 20 MINUTEN pro Kandidat. Aus technischen Gründen werden im Vorlesungsverzeichnis 30 Minuten pro Kandidat publiziert. PLEASE NOTE: The oral examination takes 20 minutes per candidate. For technical reasons, 30 minutes per candidate are published in the course catalogue.
This information can be updated until the beginning of the semester; information on the examination timetable is binding.
Learning materials
No public learning materials available.
Only public learning materials are listed.
Groups
No information on groups available.
Restrictions
There are no additional restrictions for the registration.