Universität Wien

250146 VO Algebraic topology (2007W)

6.00 ECTS (4.00 SWS), SPL 25 - Mathematik

Details

Language: German

Lecturers

Classes (iCal) - next class is marked with N

  • Monday 01.10. 11:05 - 12:35 Seminarraum
  • Wednesday 03.10. 11:05 - 11:50 Seminarraum
  • Thursday 04.10. 11:05 - 11:50 Seminarraum
  • Monday 08.10. 11:05 - 12:35 Seminarraum
  • Wednesday 10.10. 11:05 - 11:50 Seminarraum
  • Thursday 11.10. 11:05 - 11:50 Seminarraum
  • Monday 15.10. 11:05 - 12:35 Seminarraum
  • Wednesday 17.10. 11:05 - 11:50 Seminarraum
  • Thursday 18.10. 11:05 - 11:50 Seminarraum
  • Monday 22.10. 11:05 - 12:35 Seminarraum
  • Wednesday 24.10. 11:05 - 11:50 Seminarraum
  • Thursday 25.10. 11:05 - 11:50 Seminarraum
  • Monday 29.10. 11:05 - 12:35 Seminarraum
  • Wednesday 31.10. 11:05 - 11:50 Seminarraum
  • Monday 05.11. 11:05 - 12:35 Seminarraum
  • Wednesday 07.11. 11:05 - 11:50 Seminarraum
  • Thursday 08.11. 11:05 - 11:50 Seminarraum
  • Monday 12.11. 11:05 - 12:35 Seminarraum
  • Wednesday 14.11. 11:05 - 11:50 Seminarraum
  • Thursday 15.11. 11:05 - 11:50 Seminarraum
  • Monday 19.11. 11:05 - 12:35 Seminarraum
  • Wednesday 21.11. 11:05 - 11:50 Seminarraum
  • Thursday 22.11. 11:05 - 11:50 Seminarraum
  • Monday 26.11. 11:05 - 12:35 Seminarraum
  • Wednesday 28.11. 11:05 - 11:50 Seminarraum
  • Thursday 29.11. 11:05 - 11:50 Seminarraum
  • Monday 03.12. 11:05 - 12:35 Seminarraum
  • Wednesday 05.12. 11:05 - 11:50 Seminarraum
  • Thursday 06.12. 11:05 - 11:50 Seminarraum
  • Monday 10.12. 11:05 - 12:35 Seminarraum
  • Wednesday 12.12. 11:05 - 11:50 Seminarraum
  • Thursday 13.12. 11:05 - 11:50 Seminarraum
  • Monday 17.12. 11:05 - 12:35 Seminarraum
  • Monday 07.01. 11:05 - 12:35 Seminarraum
  • Wednesday 09.01. 11:05 - 11:50 Seminarraum
  • Thursday 10.01. 11:05 - 11:50 Seminarraum
  • Monday 14.01. 11:05 - 12:35 Seminarraum
  • Wednesday 16.01. 11:05 - 11:50 Seminarraum
  • Thursday 17.01. 11:05 - 11:50 Seminarraum
  • Monday 21.01. 11:05 - 12:35 Seminarraum
  • Wednesday 23.01. 11:05 - 11:50 Seminarraum
  • Thursday 24.01. 11:05 - 11:50 Seminarraum
  • Monday 28.01. 11:05 - 12:35 Seminarraum
  • Wednesday 30.01. 11:05 - 11:50 Seminarraum
  • Thursday 31.01. 11:05 - 11:50 Seminarraum

Information

Aims, contents and method of the course

The course will cover basic material from Algebraic Topology including the fundamental group, covering spaces, CW complexes, homotopy theory, higher homotopy groups, singular homology and cohomology, as well as Poincare duality. We will also discuss numerous applications of these methods, eg. a proof of the fundamental theorem of algebra using the concept of fundamental group, a proof of Brouwer's fixed point theorem using
homology theory, or a proof of the fact that subgroups of free groups are free which is based on results about covering projections.

Further information: http://www.mat.univie.ac.at/~stefan/AT.html

Assessment and permitted materials

Minimum requirements and assessment criteria

Examination topics

In der Algebraischen Topologie werden topologische Räume und stetige Abbildungen untersucht, indem den Räumen algebraische Objekte (z.B. Gruppen, Ringe oder Koerper) und den stetigen Abbildungen Homomorphismen zugeordnet werden. Diese Zuordnungen sind funktoriell, insbesondere entsprechen homoeomorphen Räemen isomorphe algebraische Objekte. Eine Analyse der algebraischen Situation liefert dann oft
Resultate über topologische Raeume und stetige Abbildungen.

Reading list

A. Hatcher, Algebraic Topology, Cambridge University Press.
Frei erhältlich unter http://www.math.cornell.edu/~hatcher/AT/ATpage.html

R. Stoecker und H. Zieschang, Algebraische Topologie. Eine Einfuehrung.
B.G. Teubner, Stuttgart.

Association in the course directory

MGET

Last modified: Mo 07.09.2020 15:40