Winter Term 2014/2015
Welcome to the course website! This course on algebraic topology is taught by Pavle Blagojević and Holger Reich and is a continuation of Topologie I. Although it is helpful to have taken Topologie I, it is not necessary.
Course Description
We understand this course as a comprehensive beginners course in algebraic topology. Although it is helpful to have taken Topologie I to follow the present course, it is not necessary. The aim of Topologie II is for you to thoroughly understand and be able to apply all notions of homology and cohomology, the cup and cross product, as well as some results on duality (for instance Poincaré duality). The course will roughly be structured as follows (as time permits):
Categories and functors, chain complexes
Singular homology, chain homotopy
Mayer-Vietoris Sequence, Jordan Curve Theorem
Reduced homology, relative homology, Alexander's theorem
Simplicial homology
Degrees, Euler characteristic, Lefschetz number, Lefschetz fixed point theorem
CW complexes
Cellular homology
Eilenberg–Steenrod axioms
Künneth Theorem
Universal Coefficient Theorem
Singular cohomology, simplicial cohomology
Cup product
Cross product, topological manifolds
Poincaré Duality
Alexander Duality
Manifolds with boundary
We recommend the books by J. Munkres ("Elements of Algebraic Topology", Addison-Wesley 1984) and A. Hatcher ("Algebraic Topology", Cambridge U Press 2002, also online) and the succinct lecture notes by J. P. May ("A Concise Course in Algebraic Topology", online).
Contact
Contact | Office Hours: | ||
Lecture | Pavle Blagojević and Holger Reich | blagojevic(at)math.fu-berlin.de, holger.reich(at)fu-berlin.de | TBA |
Tutorial | Albert Haase | a.haase(at)fu-berlin.de | Mon 14-15, 002, Arnimallee 2 |
Lectures
Lectures | ||
Wed | 10:15 - 11:45 | HS 001, Arnimallee 3 |
12:15 - 13:45 |
Tutorials and Problems
Tutorials | ||
Mon | 14:15 - 15:45 | SR 031, Arnimallee 6 |
In the tutorial, we will learn some things that will help us better understand the lecture, expand on topics from class, and occasionally review exercises.
Every week exercises will appear on this website. It is highly recommended for you to solve the most interesting and most important ones on a weekly basis. Do the other exercises if they seem challenging enough or if you don't have an idea of how to solve them immediately. Solutions to the most important exercises will appear on this website a week later. In order to encourage you to solve exercises, we will (1) periodically ask students to present solutions to an exercise in the tutorial and (2) base parts of the exam on the exercises.
Course requirements are the following: (1) You must actively participate in the course. (2) You must pass an exam at the end of the semester which alone will determine your grade. The date for the exam will be set within the first 2 weeks of class.
Problem Sheets