**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.

**Topics**

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:

**Literature**

- 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

**Exercises**

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.

**Exams**

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.