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-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