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 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 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.
 A brief introduction to characteristic classes (see also this parallel seminar on characteristic classes). Bordism and the PontrjaginThom theorem.
Here is a cumulative 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. 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. For the precise schedule, see below. Exercise sheets may be handed in jointly by at most three students.
 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.
 Exercise sheet 2 — Due on Monday, 29 October 2018. — Discussed in classes in week 4.
 Exercise sheet 3 — Due on Monday, 5 November 2018. — Discussed in classes in week 5.
 Erratum — correction to exercise 4a of sheet 3.
 Exercise sheet 4 — Due on Monday, 12 November 2018. — Discussed in classes in week 6.
 Exercise sheet 5 — Due on Monday, 19 November 2018. — Discussed in classes in week 7.
 Exercise sheet 6 — Due on Monday, 26 November 2018. — Discussed in classes in week 8.
 Exercise sheet 7 — Due on Monday, 3 December 2018. — Discussed in classes in week 9.
 Corrected version (28.11.2018) — statement of exercise 3 clarified, misleading hint and remark removed from exercise 4b, simplifying assumption added for exercise 4.
 Exercise sheet 8 — Due on Monday, 10 December 2018. — Discussed in classes in week 10.
 Corrected version (04.12.2018) — definition of Moore loop space corrected in exercise 1.
 Exercise sheet 9 — Due on Monday, 7 January 2019. — Discussed in classes in week 12.
 Exercise sheet 10 (uploaded 4 January) — Due on Monday, 14 January 2019.
 Exercise sheet 11 (uploaded 11 January) — Due on Monday, 21 January 2019.
 Exercise sheet 12 (uploaded 18 January) — Due on Monday, 28 January 2019.
 Exercise sheet 13 (uploaded 25 January) — Not to be handed in (revision sheet).
 Optional extra exercises (updated 26.11.2018) — Not to be handed in.
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 (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.


 