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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.
  • Final Exam: will be announced in due course.

                            

Assessment

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

Exercises

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.

References

  • 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)