| January 11: |
Exercises:
|
| January 13: |
Exercises:
|
| January 18: |
Introduction
Recap of general topology
Fundamental group
Brower's fixed point theorem in dimension 2
Theorem of the invariance of domain in dimension 2
Introduction to higher homotopy groups
|
| January 20: |
Singular homology (ordinary and reduced)
Hurewicz map
|
| January 25: |
Hurewicz theorem in degree 1
Homology homomorphisms induced by continuous maps
Homotopy invariance of singular homology
Short and long exact sequences of chain complexes
|
| January 27: |
This tutorial is canceled due to a strike
Exercises:
|
| February 1: |
Relative homology
Subdivision homomorphism
|
| February 3: |
Exercises:
|
| February 8: |
Theorem of small chains
Excision
Mayer-Vietoris long exact sequence
Homology of spheres
Theorem of the invariance of domain
Brower's fixed point theorem
|
| February 10: |
Exercises:
|
| February 15: |
Topological degree
Hairy ball theorem
CW complexes
|
| February 17: |
Exercises:
|
| March 1: |
Cellular homology theorem
Euler characteristic
Singular homology with coefficients
|
| March 3: |
Exercises:
|
| March 15: |
Singular cohomology
Free resolutions
Universal coefficient theorem
|
| March 17: |
Exercises:
|
| March 22: |
Proof of the universal coefficient theorem
Cup product
|
| March 24: |
Exercises:
|
| March 29: |
Crossed cup product
Künneth theorem
Topological manifolds
|
| March 31: |
Exercises:
|
| April 5: |
Orientability of topological manifolds
Fundamental class
Compactly supported cohomology
|
| April 7: |
Exercises:
|
| April 12: |
Cap product
Poincaré duality
|
| April 14: |
Exercises:
|
