Goal.
Explaining basic concepts of algebraic topology in an intuitive way.
This time.
What is...relative homology? Or: Calculations modulo subspaces.
Disclaimer.
Nobody is perfect, and I might have said something silly. If there is any doubt, then please check the references.
Disclaimer.
These videos are concerned with algebraic topology, and not general topology. (These two are not to be confused.) I assume that you know bits and pieces about general topology, but not too much, I hope.
Slides.
http://www.dtubbenhauer.com/youtube.html
Website with exercises.
http://www.dtubbenhauer.com/lecture-algtop-2021.html
Relative homology.
https://en.wikipedia.org/wiki/Relative_homology
https://math.stackexchange.com/questions/11763/meaning-of-relative-homology
https://ncatlab.org/nlab/show/relative+homology
Short and long exact sequences.
https://en.wikipedia.org/wiki/Exact_sequence
Pictures used.
https://slideplayer.com/slide/11382479/
https://en.wikipedia.org/wiki/Exact_sequence#/media/File:Illustration_of_an_Exact_Sequence_of_Groups.svg
Hatcher’s book (I sometimes steal some pictures from there).
https://pi.math.cornell.edu/~hatcher/AT/AT.pdf
Always useful.
https://en.wikipedia.org/wiki/Counterexamples_in_Topology
Mathematica.
#algebraictopology
#topology
#mathematics