401-4532-20L  Introduction to 3-Manifolds

SemesterSpring Semester 2020
LecturersM. Nagel
Periodicitynon-recurring course
Language of instructionEnglish



Courses

NumberTitleHoursLecturers
401-4532-20 VIntroduction to 3-Manifolds2 hrs
Fri11:15-13:00HG G 26.5 »
M. Nagel

Catalogue data

AbstractThis course provides an introduction to the basic notions and tools of geometric topology with a special focus on three dimensional manifolds.
ObjectiveIn 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.
ContentBackground in differential topology
Foundational results on the topology of 3–manifolds
Knots and concordance
LiteratureKnots and links by D. Rolfsen
3–Manifolds by J. Hempel
Differential topology by T. Bröcker and K. Jänich
Prerequisites / NoticeAlgebraic Topology I
Differential Geometry I

Performance assessment

Performance assessment information (valid until the course unit is held again)
Performance assessment as a semester course
ECTS credits4 credits
ExaminersM. Nagel
Typesession examination
Language of examinationEnglish
RepetitionThe performance assessment is offered every session. Repetition possible without re-enrolling for the course unit.
Mode of examinationoral 30 minutes
Additional information on mode of examinationBITTE 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

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Only public learning materials are listed.

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Offered in

ProgrammeSectionType
Mathematics MasterSelection: GeometryWInformation