V4D1 — Algebraic Topology I
Lecturer: Dr Martin PalmerAnghel
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 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 BlakersMassey theorem and the Freudenthal suspension theorem.
 Brown representability and EilenbergMacLane spaces.
 Postnikov and Whitehead towers, kinvariants.
 Quasifibrations and the DoldThom 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:
Literature
Exercises
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.
Exams
The exams are written. The dates are the following.
 First exam: 9:00–11:00, Wednesday 6 February 2019, Kleiner Hörsaal, Wegelerstr. 10.
 Here is a list of the grade boundaries for the first exam.
 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.
 Here is a list of the grade boundaries for the second exam.
 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 (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.


 