V4D1 — Algebraic Topology I
Lecturer: Dr Martin Palmer-Anghel
Assistent: Dr Benjamin Böhme
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 cumulative 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. 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.
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.