Universität Wien

250105 VO Homological algebra (2016W)

5.00 ECTS (3.00 SWS), SPL 25 - Mathematik

Details

Language: English

Examination dates

Lecturers

Classes (iCal) - next class is marked with N

Monday 03.10. 13:15 - 14:45 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 05.10. 13:30 - 14:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Monday 10.10. 13:15 - 14:45 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 12.10. 13:30 - 14:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Monday 17.10. 13:15 - 14:45 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 19.10. 13:30 - 14:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Monday 24.10. 13:15 - 14:45 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Monday 31.10. 13:15 - 14:45 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Monday 07.11. 13:15 - 14:45 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 09.11. 13:30 - 14:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Monday 14.11. 13:15 - 14:45 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 16.11. 13:30 - 14:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Monday 21.11. 13:15 - 14:45 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 23.11. 13:30 - 14:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Monday 28.11. 13:15 - 14:45 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 30.11. 13:30 - 14:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Monday 05.12. 13:15 - 14:45 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 07.12. 13:30 - 14:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Monday 12.12. 13:15 - 14:45 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 14.12. 13:30 - 14:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Monday 09.01. 13:15 - 14:45 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 11.01. 13:30 - 14:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Monday 16.01. 13:15 - 14:45 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 18.01. 13:30 - 14:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Monday 23.01. 13:15 - 14:45 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 25.01. 13:30 - 14:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Monday 30.01. 13:15 - 14:45 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock

Information

Aims, contents and method of the course

This lecture has the aim to give an introduction to homological algebra,
as it is needed for algebraic topology, commutative algebra, group theory
and number theory. The following topics are planned:
Module theory (free, projective, flat, divisible and injective modules),
categories and functors (in particular abelian categories), resolutions and
derived functors (projective and injective resolutions, homology, homotopy,
ext-functor, tor-functor), Group homology and cohomology, spectral sequences
(in particular the Hochschild-Lyndon-Serre spectral sequence), and
triangulated categories and derived categories.

Assessment and permitted materials

Written exam or oral exam after the end of the lecture

Minimum requirements and assessment criteria

Basic algebra

Examination topics

All topics covered in the lecture.

Reading list

K. S. Brown: Cohomology of groups, Graduate Texts in Mathematics, vol. 87, Springer-Verlag, New York, 1994.

H. Cartan, S. Eilenberg: Homological algebra. Princeton University Press, Princeton, NJ, 1999.

.I. Gelfand, Y.I. Manin: Methods of homological algebra, Springer, 2003.

P. Hilton; U. Stammbach: A course in homological algebra, Graduate Texts in Mathematics, Springer-Verlag,
New York, 1997.

C.A.Weibel: An introduction to homological algebra, Cambridge, 1994.

Association in the course directory

MALV

Last modified: Tu 15.02.2022 00:27