Discover the Basics of 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-algtop-2021.html

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_topology
https://en.wikipedia.org/wiki/Algebraic_topology
https://en.wikipedia.org/wiki/Differential_topology
https://en.wikipedia.org/wiki/Geometric_topology

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

Fundamental group.
https://www.math3ma.com/blog/the-fundamental-group-of-the-circle-part-1
https://www.math3ma.com/blog/the-fundamental-group-of-the-circle-part-2
https://mathworld.wolfram.com/FundamentalGroup.html
https://en.wikipedia.org/wiki/Fundamental_group

Fundamental theorem of algebra using pi_1 (I also stole some pictures from there).
http://www.homepages.ucl.ac.uk/~ucahjde/tg/html/pi1-01.html
https://math.stackexchange.com/questions/289819/fundamental-theorem-of-algebra-using-fundamental-groups

Topological data analysis.
https://brickisland.net/DDGSpring2019/wp-content/uploads/2019/01/DDG_458_SP19_Lecture02_CombinatorialSurfaces.pdf
https://towardsdatascience.com/topological-data-analysis-unpacking-the-buzzword-2fab3bb63120
https://community.wolfram.com/groups/-/m/t/2029121
https://arxiv.org/abs/1710.04019
https://en.wikipedia.org/wiki/Topological_data_analysis

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

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

#algebraictopology
#topology
#mathematics