Universität Wien
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250030 VO Homological Algebra (2024S)

3.00 ECTS (2.00 SWS), SPL 25 - Mathematik

Registration/Deregistration

Note: The time of your registration within the registration period has no effect on the allocation of places (no first come, first served).

Details

Language: English

Examination dates

Lecturers

Classes (iCal) - next class is marked with N

  • Wednesday 06.03. 15:00 - 16:30 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 13.03. 15:00 - 16:30 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 20.03. 15:00 - 16:30 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 10.04. 15:00 - 16:30 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 17.04. 15:00 - 16:30 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 24.04. 15:00 - 16:30 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 02.05. 15:00 - 16:30 Seminarraum 4 Oskar-Morgenstern-Platz 1 1.Stock
  • Wednesday 08.05. 15:00 - 16:30 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 15.05. 15:00 - 16:30 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 22.05. 15:00 - 16:30 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 29.05. 15:00 - 16:30 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 05.06. 15:00 - 16:30 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 12.06. 15:00 - 16:30 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 19.06. 15:00 - 16:30 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 26.06. 15:00 - 16:30 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 27.06. 15:00 - 16:30 Seminarraum 3 Oskar-Morgenstern-Platz 1 1.Stock

Information

Aims, contents and method of the course

Homological Algebra has its cources in works of Poincare and Hilbert. Poincare in his investigations of topological
spaces introduced homology groups which he obtained from simplicial complexes attached to the topological space.
Hilbert following his solution of the basis problem (Hilbert basis Theorem) and with the aim to make his solution
explicit introduced resolutions of ideals in polynomial rings which again are certain complexes.

The idea of investigating objects by looking at resolutions turned out to be a general abstract principle with wide applications in mathematics.
Homological Algebra is the study of this principle in a general and abstract setting. In fact Homological algebra can be
formulated and applied in arbitrary abelian categories and it may be seen as the study of abelian categories and their functors.

In the course we want to explain the abstract principle and touch on some of the techniques for computing (Co)Homolgy of
objects.

Prerequisites are very basic knowledge of modules (definition, morphisms, Sub- and Quotient modules,...) and of categories
(essentially the definition of category and functor will suffice; if we need more we will review this material).

Assessment and permitted materials

Oral exam

Minimum requirements and assessment criteria

To pass the oral exam

Examination topics

The content of the lecture course

Reading list

Weibel, C.: An Introduction to Homological Algebra
Gelfand, S., Manin, Y.: Methods of Homological Algebra
Hilton, P., Stammbach, U.: A course in Homological Algebra
Kato, G.: The Heart of Cohomology
MacLane, S.: Homology
Rotman, J.: An Introduction to Homological Algebra
Cartan, H., Eilenberg, S.: Homological Algebra

Association in the course directory

MALV

Last modified: Th 05.12.2024 08:06