What is...the Mayer-Vietoris sequence?

Goal. Explaining basic concepts of algebraic topology in an intuitive way. This time. What is...the Mayer-Vietoris sequence? Or: More than the sum of its parts!? 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 Mayer-Vietoris. https://en.wikipedia.org/wiki/Mayer%E2%80%93Vietoris_sequence https://hkt441.wordpress.com/2020/12/01/singular-homology-of-the-torus-mayer-vietoris/ Mayer-Vietories and Betti. https://math.stackexchange.com/questions/3181386/betti-numbers-inequality-and-mayer-vietoris-sequence https://www.ams.org/journals/proc/2005-133-04/S0002-9939-04-07629-4/S0002-9939-04-07629-4.pdf (Proposition 1) Pictures used. https://link.springer.com/article/10.1007/BF02307601 https://en.wikipedia.org/wiki/File:Mayer_Vietoris_sequence_boundary_map_on_torus.png 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. https://mathworld.wolfram.com/ExactSequence.html #algebraictopology #topology #mathematics