Embedded Files
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.
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)
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