Topics in Topology
Faculteit  Science and Engineering 
Jaar  2020/21 
Vakcode  WMMA02605 
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, Ktheory, three and fourdimensional manifolds, topological quantum field theory, mapping class groups, (twisted)(co)homology, HeegaardFloer 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 
