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19205401 Basismodul: Topologie I

Summer Term 2019

lecture by Prof. Dr. Holger Reich, exercises joint with Dr. Filipp Levikov

Time and place

  •  Lecture: Attention: room has been changed !

    Wednesdays, 12-14h, in seminar room 31, Arnimallee 6, and 
    Thursdays, 10-12h, in seminar room 31, Arminallee 6.

  • Exercise Session: Thursdays, 14-16, in seminar room 032, Arnimallee 6.
  • Final Exam: Wednesday, 10.7, 12:00-14:00 at Hs 2, Habelschwerdter Allee 45 (Rostlaube)

                            

Assessment

To receive credits fo the course you need to

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

If you are an FU student you only need to register for the course via CM (Campus Management), this will automatically register you for the final exam.  If you do not show up for the exam, this will count as failing it. Up to a specific deadline you may de-register from the course via CM without specifying any particular reasons. If you wish to de-register from the exam after the deadline, you should do so by contacting the exams office (Prüfungsbüro). 

If you are not an FU student, you are required to register via KVV. If you have any problems accessing it, please email F. Levikov.

Exercises      

Problem sets will be put online every Wednesday/Thursday and can be found under Assignements in the KVV portal. Solutions (in pairs!) are (presumably) 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. Group actions on topological spaces. 
3. Gluing constructions.
4. Homotopies between continuous maps, degree of a map, fundamental group.
5. Seifert-van Kampen Theorem. 
6. Covering spaces.

References

  • Tammo tom Dieck: Topologie, De Gruyter Lehrbuch
  • Allen Hatcher: Algebraic Topology, Chapter I. Also available online from the author's website (english)
  • Klaus Jänich: Topologie, Springer-Verlag (german, english)
  • Gerd Laures, Markus Szymik: Grundkurs Topologie, Spektrum Akademischer Verlag (german)
  • James R. Munkres: Topology, Prentice Hall (english)