Lecturer: Daniel Kasprowski
Office: 3.022
eMail: kasprowski at uni-bonn.de
Assistant: Fabian Hebestreit
Office: 3.023
eMail: f.hebestreit at math.uni-bonn.de
Slot 1: mondays, 10am - 12pm
Slot 2: fridays, 2pm - 4pm
Location: kleiner Hörsaal
Excercise Sessions:
Group 1: fridays, 12pm - 2pm
Location: Room 0.006
Tutor: Tobias Fleckenstein
eMail: s4toflec at uni-bonn.de
Group 2: mondays, 8am - 10am
Location: Room 0.003
Tutor: Florian Kranhold
eMail: kranhold at math.uni-bonn.de
Group 3: tuesdays, 10am - 12pm
Location: Room 0.006
Tutor: Robin Stoll
eMail: s6rostol@uni-bonn.de

Topology II


The post-exam review for the second exam will take place on tuesday, October 1st, 2pm - 2:30pm in Daniel's office. The solutions are also available now.


The exercise sessions will start on Friday, April 5th.
In the lecture we will cover standard material of the algebraic topology curriculum, building on the lecture Topology I. More specifically we plan to cover the following topics (roughly in order):

  • Homology of products
  • Homology of manifolds, Poincaré duality
  • Higher homotopy groups
  • Fibrations and Cofibrations

  • Here are the notes for the last two lectures.

    The exam dates are July 26th, 13pm-16pm, Hörsaal der Anatomie A, and September 27th, 9am-12pm, Kleiner Hörsaal.
    Here you can find the assignment for the exercise groups.

    Exercise sheets

    The exercise sheets will usually appear before wednesdays and solutions have to be handed in before wednesday 11:30am the following week . This can be done either in the lecture, in the exercise sessions, or directly to Daniel or Fabian between 10:30 and 11:30. Florian has written up rough notes on the solutions.

    Sheet no 1, Solutions
    Sheet no 2, Solutions
    Sheet no 3, Solutions to 1,2, Counterexamples to 3,4
    Sheet no 4, Solutions
    Sheet no 5, Solutions
    Sheet no 6, Solutions
    Sheet no 7, Solutions
    Sheet no 8, Solutions
    Sheet no 9, Solutions
    Sheet no 10, Solutions
    Sheet no 11, Solutions
    Exam 1 with solutions
    Exam 2 with solutions

    Recommended Literature

  • Ausoni: Algebraische Topologie / Algebraische Topologie II Kurzskripten (notes for a lecture course, available here and here, in german)
  • tom Dieck: Topologie / Algebraic Topology
  • Hatcher: Algebraic Topology (available here)
  • Lück: Algebraische Topologie: Homologie und Mannigfaltigkeiten (in german)
  • Waldhausen: Algebraische Topologie / Algebraische Topologie II Skripten (notes for a lecture course, available here, in german)
  • Whitehead: Elements of Homotopy Theory
  • Riehl: A leisurely introduction to simplicial sets, available here