Algebraic Topology 1
For this course, I will sometimes make use of other lecture notes, which have been written by Ieke Moerdijk and Moritz Groth for a course given at Nijmegen University. I gratefully acknowledge their courtesy in letting me use them.
The course starts on October 7th and it runs on Mondays (lectures) and Thursdays (exercises), from 17:20 to 18:50. The classes on the 14th and 17th of October will not run, but we will make them up later before the end of the course.
This will be a written exam with similar exercises as the ones we have done during tutorials. We will also see some more exercises in the 6th to 10th week of January.
Lecture 1: Categorical language and the notion of homotopy (pdf, up to Def. 1.7 included)
Exercise sheet 1 (pdf)
Lecture 2: "The fundamental group(oid) functor" (pdf)
Exercise sheet 2 (pdf)
Lecture 3: "Spaces of maps, loop spaces and reduced suspensions " (pdf)
Exercise sheet 3 (pdf)
Lecture 4: "Covering spaces and fibrations" (pdf)
Exercise sheet 4 (pdf)
Lecture 5: "Fibrations and fundamental groups" (pdf)
Exercise sheet 5 (pdf)
Lecture 6: "Seifert-Van Kampen's theorem" (pdf)
Exercise sheet 6 (pdf)
Lecture 7: "Singular homology" (pdf)
Exercise sheet 7 (pdf)
Lecture 8:"Low dimensional identifications" (pdf)
Exercise sheet 8 (pdf)
Lecture 9: "Relative singular homology and the long exact sequence of a pair" (pdf)
Exercise sheet 9: fill in the gaps in the proofs given in class
Lecture 10: "Homotopy invariance of singular homology and (reduced) homology groups of spheres" (pdf)
Lecture 11: "Excision property and Mayer-Vietoris sequence" (pdf)
Exercise sheet 12: "Calculations with the Mayer-Vietoris sequence" (pdf)
Some examples: Torus (ex 2), Torus + Mobius band (ex 7)
Solutions (week 12): (pdf)
Exercise sheet 13: "Recap" (pdf)