Topology II (V3D2/F4D1)

Sommersemester 2018

Lecturer	Dr. Irakli Patchkoria (Email: irpatchk (add ''at''math.uni-bonn.de))
Assistent	Dr. Christian Wimmer (Email: wimmer (add ''at''math.uni-bonn.de))
Time and Place	Mondays, 10:15-12:00 in Zeichensaal (Wegelerstr. 10) Wednesdays, 8:15-10:00 in Kleiner Hörsaal (Wegelerstr. 10)

Topics

These lectures will cover some classical topics in Topology. We will continue studying cohomology and higher homotopy groups which were introduced in Topology I. The main topics of the lectures are: Poincaré duality and its applications, Hurewicz theorem, the theory of fibrations. There will be a lot of focus on examples and computations.

Literature

A. Hatcher, Algebraic Topology

J. Milnor and J. Stasheff, Characteristic Classes (Princeton University press)

G. Bredon, Topology and Geometry (Springer)

S. Schwede, Kohomologie

F. Waldhausen, Algebraische Topologie II

A. Dold, Lectures on Algebraic Topology (Springer)

Exams

There will be oral exams in the last week of the Semester (16.07 to 20.07). Requirements for admission to the exams are:

At least half of the credits from the exercise sheets

Having presented at least two exercises on the blackboard during the exercise sessions

All exams will take place in Room 4.006, Endenicher Allee 60.
The second exams will take place on September 27-28th.
If you want to take an exam in September, then please write an email (preferably after 20.07.2018) to Irakli Patchkoria at irpatchk''at''math.uni-bonn.de.

Further options

If you want to learn more topology after our class is done, you can attend some more lectures and seminars in the next semester. Algebraic Topology I is the most obvious choice. There are also several interesting seminars offered in the next semester. For example, a Seminar on Characteristic Classes organized by F. Hebestreit would be a great choice. After Topology II you have a very good background for participating in this seminar.

Exercises

There will be two exercise groups and each group will meet once a week:

Group I (Thorben Kastenholz) : Tuesday 10:15-12:00 in SR 0.006

Group II (Michael Stahlhauer) : Friday 12:15-14:00 in SR 0.006

The exercise classes will start in the second week (the first sessions will be on 17.04 and 20.04).

The new exercise sheets will be available here for download on Fridays. The completed exercises have to be handed in 10 days later before the Monday lecture. Exercise sheets may be handed in jointly by at most three students.

Exercises 1

Exercises 2

Exercises 3

Exercises 4

Exercises 5

Exercises 6

Exercises 7

Exercises 8

Exercises 9

Exercises 10

Exercises 11

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