Martin David Palmer -- Lecture course -- Algebraic Topology I
Algebraic Topology I
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V4D1 — Algebraic Topology I

Lecturer: Dr Martin Palmer-Anghel
Assistent: Dr Benjamin Böhme
Wintersemester 2018/2019
Lectures: Monday 14–16, Wednesday 8–10
(First lecture: Monday 8th October 2018)
Room: Zeichensaal (Wegelerstr. 10)
Link to the official course webpage in basis.


This is a continuation of the course Topology II in Sommersemester 2018, focused on homotopy theory. The main topics will be the following (*subject to modification as the lectures progress!*).

  • A brief recollection of some homotopy theory that was covered in the lectures Topology I and Topology II.
  • Fibrations and cofibrations, homotopy (co)fibres.
  • The Blakers-Massey theorem and the Freudenthal suspension theorem.
  • Brown representability and Eilenberg-MacLane spaces.
  • Postnikov and Whitehead towers, k-invariants.
  • Quasifibrations and the Dold-Thom theorem.
  • Serre classes and rational homotopy groups of spheres.
  • Principal bundles, vector bundles, classifying spaces.
  • A brief introduction to characteristic classes (see also this parallel seminar on characteristic classes). Bordism and the Pontrjagin-Thom theorem.

Here is a brief outline of the topics covered in the lectures so far:


  • Tammo tom Dieck, Algebraic Topology
  • Allen Hatcher, Algebraic Topology
  • John Milnor and Jim Stasheff, Characteristic Classes
  • Robert Switzer, Algebraic Topology — Homotopy and Homology
  • George W. Whitehead, Elements of Homotopy Theory


There are two exercise classes, taking place once per week, starting in the second week of the semester.

  • Friday 10–12 — Daniel Brügmann — seminar room 1.008.
  • Friday 12–14 — Benjamin Ruppik — seminar room 0.011.

The exercise sheets will be uploaded here on Fridays.

Exercise sheet n (uploaded on the Friday of the nth week of the semester, for positive n) should be handed in before the lecture on Monday afternoon of week n+2. Exercise sheets may be handed in jointly by at most three students. There is also a preliminary exercise sheet 0, not to be handed in, which will be discussed in the exercise classes in week 2.

  • Exercise sheet 0 — Not to be handed in. — Discussed in classes in week 2.
  • Exercise sheet 1 — Due on Monday, 22 October 2018. — Discussed in classes in week 3.


The exams will be written. The dates are the following.

  • First exam: 9:00–11:00, Wednesday 6 February 2019, Kleiner Hörsaal, Wegelerstr. 10.
  • Klausureinsicht (exam review): 14:00–15:00, Thursday 7 February 2019, seminar room 0.011.
  • Second exam: 9:00–11:00, Wednesday 13 March 2019, Kleiner Hörsaal, Wegelerstr. 10.
  • Klausureinsicht (exam review): 14:00–15:00, Thursday 14 March 2019, seminar room 0.011.

As usual, the requirements for admission to the exam are:

  • Obtaining at least half of the credits from the exercise sheets.
  • Presenting at least two exercises on the blackboard during the exercise sessions.