Group Cohomology, SS 2019

Prof. Dr. C. Löh / Dr. D. Fauser / J. Witzig

News

Group Cohomology

Group cohomology is an invariant that connects algebraic and geometric properties of groups in several ways. For example, group cohomology admits descriptions in terms of homological algebra and also in terms of topology. Different choices of coefficients for group cohomology leads to different invariance properties, whence to different types of applications. Group cohomology naturally comes up in algebra, topology, and geometry. For example, group cohomology allows to In this course, we will introduce the basics of group homology and cohomology, starting with elementary descriptions and calculations. Depending on the background of the audience, we will then either focus on a more algebraic perspective or on a more topological one.

If all participants agree, this course can be held in German; solutions to the exercises can be handed in in German or English.

Lecture notes: pdf. Topics covered so far:
comments:

Time/Location

Monday, 10--12, M 102,
Thursday, 10--12, M 104.

Exercise classes

group 1: Thursday, 12--14, M 102
group 2: Friday, 8:30--10, H 32

Exercise sheets

Solutions can be submitted in English or German and in teams of up to two people. Please do not forget to add your name to all your submissions!

Sheet 1, of April 29, 2019, submission before May 6, 2019 (10:00) will be discussed in the exercise classes on May 9/10
Sheet 2, of May 6, 2019, submission before May 13, 2019 (10:00) will be discussed in the exercise classes on May 16/17
Sheet 3, of May 13, 2019, submission before May 20, 2019 (10:00) will be discussed in the exercise classes on May 23/24
Sheet 4, of May 20, 2019, submission before May 27, 2019 (10:00) will be discussed in the exercise classes on May 29(!)/31
Sheet 5, of May 27, 2019, submission before June 3, 2019 (10:00) will be discussed in the exercise classes on June 6/7
Sheet 6, of June 3, 2019, submission before June 11(!), 2019 (10:00) will be discussed in the exercise classes on June 13/14
Sheet 7, of June 10, 2019, submission before June 17, 2019 (10:00) will be discussed in the exercise classes on June 19/21
Sheet 8, of June 17, 2019, submission before June 24, 2019 (10:00) will be discussed in the exercise classes on June 27/28
Sheet 9, of June 24, 2019, submission before July 1, 2019 (10:00) will be discussed in the exercise classes on July 4/5
Sheet 10, of July 1, 2019, submission before July 8, 2019 (10:00) will be discussed in the exercise classes on July 11/12
Sheet 11, of July 8, 2019, submission before July 15, 2019 (10:00) will be discussed in the exercise classes on July 18/19
Sheet 12, of July 15, 2019, submission before July 22, 2019 (10:00) will be discussed in the exercise classes on July 25/26

Etudes

These etudes help to train elementary techniques and terminology. These problems should ideally be easy enough to be solved within a few minutes. Solutions are not to be submitted and will not be graded.

Sheet 0, of April 25, 2019, no submission, will be discussed in the exercise classes on May 2/3.
Sheet 1, of May 2, 2019 no submission
Sheet 2, of May 9, 2019 no submission
Sheet 3, of May 16, 2019 no submission
Sheet 4, of May 23, 2019 no submission
Sheet 5, of May 30, 2019 no submission
Sheet 6, of June 6, 2019 no submission
Sheet 7, of June 13, 2019 no submission
Sheet 8, of June 20, 2019 no submission
Sheet 9, of June 27, 2019 no submission
Sheet 10, of July 4, 2019 no submission
Sheet 11, of July 11, 2019 no submission

Literature

This course will not follow a single book. Therefore, you should individually compose your own favourite selection of books.
A list of suitable books can be found in the lecture notes.

Prerequisites

All participants should have a firm background in Analysis I/II (in particular, basic point set topology, e.g., as in Analysis II in WS 2011/12), in Linear Algebra I/II, and basic knowledge in group theory (as covered in the lectures on Algebra).
Knowledge about manifolds as in Analysis IV is not necessary, but helpful.
Knowledge about basic homological algebra (as in the last two weeks of Kommutative Algebra) is not necessary, but helpful.
Knowledge on algebraic topology (as in the course in WS 18/19) is not necessary, but helpful.

Exams

Please read the information on organisation and formalities of this course.

Dates for the oral exams (25 minutes): Registration details: . If you prefer to take a combined oral exam on Algebraic Topology and Group Cohomology, please contact me.

Last change: July 15, 2019