Topics in Topology

Faculteit Science and Engineering
Jaar 2021/22
Vakcode WMMA026-05
Vaknaam Topics in Topology
Niveau(s) master
Voertaal Engels
Periode semester II a
ECTS 5
Rooster rooster.rug.nl

Uitgebreide vaknaam Topics in Topology
Leerdoelen At the end of the course, the student is able to:
1. Reproduce key properties and examples of topological spaces and their use in other fields of mathematics.
2. Apply key concepts, such as basic homotopy and homology theory to solve problems.
3. Study a subject from the field of topology at research level by her/himself guided by the lecturer.
4. Give a professional oral presentation on a specific subject in topology and explain the subject to his/her peers (which includes answering questions).
Omschrijving Topology is a broad subject with strong ties to many areas of mathematics. At its core it is an extension of set theory to provide a basic language for global and course geometric notions of when things are close whether they contain holes. Elementary algebraic tools such as groups and vector spaces allow one to study topological spaces effectively using homology and homotopy. After treating basic notions we focus on a specific topic in topology and study it in greater depth by means of lectures and student presentations. Possible topics include: knot theory, homotopy theory, K-theory, three and four-dimensional manifolds, topological quantum field theory, mapping class groups, (twisted)(co)homology, Heegaard-Floer homology etc.
Uren per week
Onderwijsvorm Bijeenkomst (S), Opdracht (ASM), Werkcollege (T)
Toetsvorm Opdracht (AST), Practisch werk (PR), Presentatie (P)
(Final grade = 50% presentations, 25% practical work, 25 % homework and lecture notes/slides presentations)
Vaksoort master
Coördinator dr. R.I. van der Veen
Docent(en) dr. R.I. van der Veen
Entreevoorwaarden Knowledge assumed of: Introduction to metric and topological spaces, linear algebra, group theory, multivariable analysis. Analysis on manifolds is recommended but not required.
Opmerkingen
Opgenomen in
Opleiding Jaar Periode Type
MSc Mathematics: Mathematics and Complex Dynamical Systems - semester II a keuzegroep
MSc Mathematics: Science, Business and Policy  (Science, Business and Policy: Mathematics and Complex Dynamical Systems) - semester II a keuzegroep