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19215101 Aufbaumodul: Topologie III "Homotopy Theory"

Summer term 2017

lecture by Prof. Dr. E. Vogt, exercises joint with Dr. Filipp Levikov

  • Time and place: 18.04-01.06. Tuesdays 12-14 in SR 210 Arnimallee 3, Thursdays 12-14 in SR 140 Arminallee 7. 

  • Exercise Session: Thursdays 14-16, SR 007/008 Arnimallee 6.

Course Overview

This will be an introduction to homotopy theory. We will cover: Higher homotopy groups, cofiber and fiber sequences, cofibrations, fibrations, excision for homotopy groups with applications to calculating homotopy groups of spaces important for topology and geometry, CW-approximation and cellular approximation, Whitehead Theorem, Hurewicz Theorem, spectra and their relation to cohomology and homology theories.


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.

To receive credits fo the course you need to

  • actively participate in the exercise session and successfully solve the weekly exercises (obtain at least 50% of total points)
  • pass the final exam

To register for the final exam it suffices to register for the course via CMS.

Exercise sheets

Problem sets will be put online every Wednesday/Thursday and can be found under Assignements in the KVV portal. Solutions are due by 2 pm on Thursday of the following week  –  please use the corresponding mailbox on the ground floor in Arnimallee 3-5.


Tammo tom Dieck, Algebraic Topology, EMS Textbooks in Mathematics, 2008, Chapters 4 - 8;

Allen Hatcher, Algebraic Topology, Chapter 4. Also available online from the author's website.

John Peter May, A Concise Course in Algebraic Topology, The University of Chicago Press, 1999. Also available online from the author's website