Group Cohomology, SS 2019

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

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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.

Time/Location

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

Exercise classes

tba

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.

Last change: January 12, 2019