Topology 2 (SoSe 2023)

• Time and place: Lectures: Wed, 10:00 -12:00 and Thu, 12:00 -14:00 (Room B 251)
  Exercises: TBD (the schedule for the exercise classes will be decided in the first lecture)
• Exercise classes: The weekly homework assignments will be discussed in the exercise classes. Homework assignments will be posted only on moodle.
• Contents: Topics will include CW complexes, cellular homology, universal coefficient theorems, Kunneth theorems, cohomology, cup and cap products, orientations, Poincare duality and further selected topics such as Steenrod operations or Thom isomorphism. Please find a more detailed syllabus on moodle. The key to enroll yourself is thom. Exercise sheets, perhaps lecture notes, and announcements will only be posted on moodle.
• Audience: The course is intended for Master students of mathematics or physics. Of course, everyone who is interested is welcome to attend.
• Language: The course will be taught in English.
• Prerequisites: Topology 1 (the lecture notes of last semester's Topology 1 will be made available on moodle).
• References: There are many good textbooks on the subject, and the lectures will be drafted from several ones:
  • A. Dold, Lectures on Algebaric Topology, Springer. The relevant chapters are V - VIII.
  • H. Miller, Lectures on Algebraic Topology, World Scientific Publishing. The relevant parts are Sections 2 and 3, and selected topics from later sections.
  • A. Hatcher, Algebraic Topology, Cambridge University Press. The relevant parts are Section 2.2, Chapter 3 and selected topics from Chapter 4. The book is a little chatty in style and contains lots of good exercises. Available for free.