Algebraic Topology II - M2 - 8EC

Prerequisites
- CW-complexes and singular homology to the extent treated in the Algebraic Topology 1 course taught in the fall; see the lectures notes by Steffen Sagave available at https://www.math.ru.nl/~sagave/teaching/at-lecturenotes-2023.pdf
- Point set topology and the fundamental group to the extent these topics were already used in the Algebraic Topology 1 course.
- Basis knowledge about algebra and categories to the extent that one is familiar with the concepts of rings, modules, their tensor product, functors and natural transformations; see for example the lecture notes "Modules and Categories" by Lenny Taelman, available at https://staff.fnwi.uva.nl/l.d.j.taelman/ca.pdf

Aim of the course
This course covers advanced topics in Algebraic Topology, which may vary from year to year and build on the foundations provided by the Algebraic Topology 1 course from the fall.
The topics covered in this edition of Algebraic Topology 2 are basics of cohomology groups, orientations of manifolds and Poincare-duality, fibrations and cofibrations, Eilenberg-Mac Lane spaces, and Steenrod squares.

  • Basics of cohomology groups
  • Orientations of manifolds and Poincare-duality
  • Fibrations and cofibrations
  • Eilenberg-Mac Lane spaces
  • Steenrod squares

Lecturers
- Lennart Meier (UU)
- Steffen Sagave (RU)