What is...algebraic topology?

Goal.
Explaining basic concepts of algebraic topology in an intuitive way.

This time.
What is...algebraic topology? Or: Translating from topology to algebra.

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-a...

Material used.
https://en.wikipedia.org/wiki/Topology

The four main fields (I also stole some pictures from there).
https://en.wikipedia.org/wiki/General...
https://en.wikipedia.org/wiki/Algebra...
https://en.wikipedia.org/wiki/Differe...
https://en.wikipedia.org/wiki/Geometr...

Awesome fundamental group animations (and other great stuff).
https://math.unice.fr/~indira/Mygifs....

Fundamental group.
https://www.math3ma.com/blog/the-fund...
https://www.math3ma.com/blog/the-fund...
https://mathworld.wolfram.com/Fundame...
https://en.wikipedia.org/wiki/Fundame...

Fundamental theorem of algebra using pi_1 (I also stole some pictures from there).
http://www.homepages.ucl.ac.uk/~ucahj...
https://math.stackexchange.com/questi...

Topological data analysis.
https://brickisland.net/DDGSpring2019...
https://towardsdatascience.com/topolo...
https://community.wolfram.com/groups/...
https://arxiv.org/abs/1710.04019
https://en.wikipedia.org/wiki/Topolog...

Venn diagrams in latex.
https://latexdraw.com/how-to-draw-ven...

Hatcher’s book (I sometimes steal some pictures from there).
https://pi.math.cornell.edu/~hatcher/...

Always useful.
https://en.wikipedia.org/wiki/Counter...

#algebraictopology
#topology
#mathematics