Algebraic Topology
Faculteit  Science and Engineering 
Jaar  2022/23 
Vakcode  WBMA05805 
Vaknaam  Algebraic Topology 
Niveau(s)  bachelor 
Voertaal  Engels 
Periode  semester I a 
ECTS  5 
Rooster  rooster.rug.nl 
Uitgebreide vaknaam  Algebraic Topology  
Leerdoelen  At the end of the course, the student is able to: 1. Construct new spaces using the quotient topology 2. Compute the homology and fundamental group of simple spaces 3. Judge when two maps are homotopic 4. Classify surfaces 5. Explain how the techniques of topology apply to other fields of mathematics 

Omschrijving  In topology we study only the most fundamental geometric properties of an object: How many pieces does it consist of? Does it have a boundary? Does it have any holes? What is its dimension? Topology applies to objects coming from dynamical systems and geometry to data analysis and number theory. The simplest properties of a space have the largest impact and often the objects one deals with in practice are so complicated that even computing the topological properties is a great challenge. In this course we will start by cutting and pasting abstract spaces. For example an abstract surface is obtained by gluing together triangles. What surfaces are possible up to continuous deformations? We will develop two algebraic techniques for studying the topology of a space: they are called the fundamental group and homology. The first deals with walking paths through the space while the latter studies the difference between being the boundary of something and having no boundary at all. 

Uren per week  
Onderwijsvorm  Hoorcollege (LC), Werkcollege (T)  
Toetsvorm 
Opdracht (AST), Schriftelijk tentamen (WE)
(Let E be the grade of the final exam and H be the grade for the homework solutions. Then the final grade is the maximum of E and (4E+H)/5.) 

Vaksoort  bachelor  
Coördinator  dr. R.I. van der Veen  
Docent(en)  O. Lorscheid, PhD. ,dr. R.I. van der Veen  
Verplichte literatuur 


Entreevoorwaarden  The course assumes knowledge from the following courses: Group theory, Metric and topological spaces  
Opmerkingen  
Opgenomen in 
