Topology 1 (WiSe 2022/23)
- Time and place: Lectures: Wed, 10:00 -11:35 and Fri, 08:30 -10:00 (Room B 132)
Exercises: Wed, 14-16 (Room B 039) and Fri, 12-14 ct (Room B 252) - Exercise classes: The weekly homework assignments will be discussed in the exercise classes. There will be two groups, one with Jonas Stelzig and one with Simon Gritschacher. Homework assignments will be posted only on moodle.
- Contents: We will begin with a brief introduction to point-set topology, and then discuss various topics in algebraic topology (fundamental group, covering spaces, homology theory, orientability and fundamental class). A more detailed syllabus will be added soon. Please also register on moodle. The key to enroll yourself is poincare. Exercise sheets, perhaps lecture notes, and announcements will only be posted on moodle.
- Audience: The course is intended for students of mathematics or physics in the third year or higher. Of course, everyone who is interested is welcome to attend.
- Language: The course will be taught in English.
- Prerequisites: Basic courses in calculus and (linear) algebra.
- References: There are many good textbooks on the subject, and the lectures will be drafted from several ones. The lectures on point-set topology will be based on the following two books:
- K. Jänich, Topologie, Springer Verlag. (German, but there is an English translation).
- J. Munkres, Topology, Pearson.
- A. Hatcher, Algebraic Topology, Cambridge University Press. The relevant parts are chapters 1 and 2. The book is a little chatty in style and contains lots of good exercises. Available for free.
- W.S. Massey, A Basic Course in Algebraic Topology, Springer Verlag. The relevant chapters are II-XI.
- J.P. May, A Concise Course in Algebraic Topology, University of Chicago Press. This is a cute little book. I wouldn't recommend it as the primary reference, because it leans towards some topics that won't be covered in our course, but still great for those who are interested.
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