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 was a continuation of the course Topology II in Sommersemester 2018, focused on homotopy theory. The main topics were the following.

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.

Here is a detailed outline of the topics covered in the lectures:

There were 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 are uploaded here on Fridays. The general pattern is that 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.

Corrected version (28.11.2018) — statement of exercise 3 clarified, misleading hint and remark removed from exercise 4b, simplifying assumption added for exercise 4.

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

Obtaining at least half of the credits from the exercise sheets (from sheets 1–11, each of which has 20 points available, so the threshold is at least 110/220 points).

Presenting at least two exercises on the blackboard during the exercise sessions.