Prof. D. Kotschick: Topology I

• Time and Place: Tuesdays and Thursdays 10-12, room C123
  
• Exercise classes: There will be multiple sessions, e.g. Tuesday 2-4 PM in B 041, Wednesday 2-4 PM in B 046 and Wednesday 4-6 in B041, as well as online sessions at times to be determined. Due to limitations on the numbers of people allowed at the in person sessions, you need to register for these classes in moodle.
  
• Content: This is the first half of a full-year course on topology. We will start with a rapid review of some basic point-set topology, and then proceed to discuss mostly algebraic topology. While there will be some geometric topology early on, essentially no differential topology will be discussed. The topics for the first semester are: surfaces as two-dimensional abstract manifolds, the fundamental group, applications to group theory, covering spaces, and homology theory, up to a computation of the homology of CW complexes.
  So far, the plan for the second semester is to discuss homology with coefficients, cohomology theory (including products), and duality theorems for cohomology. This may change depending on how we manage the first semester.
• For: Students of mathematics or physics in the third year or higher.
  
• Prerequisites: Basic courses in calculus and (linear) algebra.
  
• Language: This course will be taught in English.
• Exam: There will be an exam in February, details to be announced via moodle.
• References: For general background and introductory material you may consult
  K. Jänich: Topologie, Springer Verlag. (There is an English translation of this.)  
  The main part of the course will follow Chapters I to IX of the book
  W. S. Massey: A basic course in algebraic topology, Springer GTM, Springer Verlag 1991. (We have multiple copies of this in the library, which you can borrow for your use. I have ordered online access, and will notify the participants when this becomes available.) Update (29 Oct): Today I was informed by the university library that they have been unable to purchase online access from Springer. Please do not ask me how this is possible. After receiving their message, I went to the Springer website and purchased the ebook myself.
  A standard source for algebraic topology is the book
  A. Hatcher: Algebraic Topology, Cambridge University Press. (This contains all the material that is in Massey, and you are free to use it, but I will stick to Massey.)
  
• Special note because of Covid-19 restrictions: This course will be taught in a hybrid manner, mixing online instruction with in person meetings (to the extent that the latter are allowed). I will make an effort to offer as much in person teaching as possible. Nevertheless, it should be possible to also follow the course exclusively online, though this may turn out to be more difficult.
  To register for the course and obtain access to course materials it is necessary to sign up via moodle under this link. The password for logging in is Massey. At the time of registration please choose which exercise class you want to take part in, and answer the question about being or not being present in Munich. This will help us plan the further offerings in coming weeks.
  If for some reason you cannot sign up in moodle, but still want to take the course, please write to Dr. J. Stelzig at Jonas.Stelzig@math.lmu.de .