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19205401 Basismodul: Topologie I

Summer Term 2022

lecture by  Dr. Gabriel Angelini-Knoll

Time and place

  •  Lecture:  Tuesdays, 08-10h, in SR 031, Arnimallee 6, and
                     Thursdays, 10-12h, in SR 031, Arnimallee 6.

  • Exercise Session: Thursdays, 14:00-16:00h, in SR 032, Arnimallee 6.
  • Additional exercise Sessions: Tuesday, June 14th, 16:00-18:00h, and
                                                        Tuesday, June 28th, 16:00-18:00h,
                                                        both in SR 032, Arnimallee 6.

  • Final Exam: Tuesdays, July 26th, 14:00-16:00h, lecture hall, Takustr. 9.
  • Exam viewing: Friday, July 29th, 10:00-12:00h, SR 031, Arnimallee 6.
  • Follow-up Exam: Thursday, August 25th, 14:00-16:00h, lecture hall 001, Arnimallee 3-5.



To receive credits for the course you need to

  • actively participate in the exercise session 
  • work on and successfully solve the weekly exercises 
  • pass the final exam


Problem sets will be put online every Wednesday and can be found under Assignements in MyCampus/Whiteboard. Solutions (in small groups!) are due by 2 pm on Thursday of the following week  –  please submit either using the corresponding mailbox on the ground floor in Arnimallee 3-5 or in the exercise session.

Course Overview

1. Basic notions. Topological spaces, products, coproducts, quotients, compactness. 
2. Gluing constructions.
3. Homotopies between continuous maps, degree of a map, fundamental group.
4. Seifert-van Kampen Theorem. 
5. Covering spaces.


  • Tammo tom Dieck: Algebraic Topology, EMS Textbooks in Mathematics
  • Allen Hatcher: Algebraic Topology, Chapter I. Also available online from the author's website (english)
  • J.P. May: A Concise Course in Algebraic Topology, Chicago Lectures in Mathematics
  • James R. Munkres: Topology, Prentice Hall (english)