Universität Wien
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250051 VO Algebraic topology (2013S)

6.00 ECTS (4.00 SWS), SPL 25 - Mathematik

Further information: http://www.mat.univie.ac.at/~stefan/AT13.html

Details

Language: German

Examination dates

Lecturers

Classes (iCal) - next class is marked with N

  • Tuesday 05.03. 10:15 - 11:45 Seminarraum
  • Thursday 07.03. 10:15 - 11:45 Seminarraum
  • Tuesday 12.03. 10:15 - 11:45 Seminarraum
  • Thursday 14.03. 10:15 - 11:45 Seminarraum
  • Tuesday 19.03. 10:15 - 11:45 Seminarraum
  • Thursday 21.03. 10:15 - 11:45 Seminarraum
  • Tuesday 09.04. 10:15 - 11:45 Seminarraum
  • Thursday 11.04. 10:15 - 11:45 Seminarraum
  • Tuesday 16.04. 10:15 - 11:45 Seminarraum
  • Thursday 18.04. 10:15 - 11:45 Seminarraum
  • Tuesday 23.04. 10:15 - 11:45 Seminarraum
  • Thursday 25.04. 10:15 - 11:45 Seminarraum
  • Tuesday 30.04. 10:15 - 11:45 Seminarraum
  • Thursday 02.05. 10:15 - 11:45 Seminarraum
  • Tuesday 07.05. 10:15 - 11:45 Seminarraum
  • Tuesday 14.05. 10:15 - 11:45 Seminarraum
  • Thursday 16.05. 10:15 - 11:45 Seminarraum
  • Thursday 23.05. 10:15 - 11:45 Seminarraum
  • Tuesday 28.05. 10:15 - 11:45 Seminarraum
  • Tuesday 04.06. 10:15 - 11:45 Seminarraum
  • Thursday 06.06. 10:15 - 11:45 Seminarraum
  • Tuesday 11.06. 10:15 - 11:45 Seminarraum
  • Thursday 13.06. 10:15 - 11:45 Seminarraum
  • Tuesday 18.06. 10:15 - 11:45 Seminarraum
  • Thursday 20.06. 10:15 - 11:45 Seminarraum
  • Tuesday 25.06. 10:15 - 11:45 Seminarraum
  • Thursday 27.06. 10:15 - 11:45 Seminarraum

Information

Aims, contents and method of the course

This introductory course will cover basic material from Algebraic Topology including the fundamental group, covering spaces and singular homology. 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.

Assessment and permitted materials

Oral exam.

Minimum requirements and assessment criteria

To become acquainted with basic methods in Algebraic Topology and their application.

Examination topics

Algebraic Topology studies topological spaces and continuous maps by associating algebraic objects (eg. groups, rings, or algebras) to spaces, and homomorphisms to continuous maps.

Reading list

[1] Dold, Lectures on Algebraic Topology.
[2] Hatcher, Algebraic Topology.
freely available at: http://www.math.cornell.edu/~hatcher/AT/ATpage.html
[3] Jänich, Topologie.
[4] May, A Concise Course in Algebraic Topology.
[5] Stoecker und Zieschang, Algebraische Topologie. Eine Einfuehrung.
[6] tom Dieck, Algebraic topology.

Association in the course directory

MGET

Last modified: Mo 07.09.2020 15:40