Course on Homological Algebra (first semester 2012/2013)
This is a course taught by Urs Schreiber.
Time and place: Tuesday and Thursday, 13.30-15.30, room: Linnaeus Building, lecture room 9 (LIN9)
Prerequisites: Basic knowledge of algebra (linear algebra, symmetry) and topology.
Exams: Take-home exam.
This course is an introduction to basic concepts in homological algebra; intended for students with just a basic background in algebra.
Homological algebra studies certain sequences of abelian groups called chain complexes. An archetypical example is the complex of linear combinations of simplices in a topological space. To such complexes one may assign an invariant called their homology, which gives the subject its name. It turns out that homology groups are of wide applicability throughout mathematics. Notably they can be used for showing that certain algebraic structures exist at all, and if so, how many choices there are. Homological algebra provides tools for studying homology generally and by explicit computation, not only in topology but also homology of groups, of Lie algebras, and of various structures in algebraic geometry.
In this course we introduce the basics of these tools.
Weibel: An introduction to homological algebra
Schreiber: Lecture notes
(Under this link you will find many more references.)
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