What is...Alexander duality? скачать в хорошем качестве

What is...Alexander duality?

Goal. Explaining basic concepts of algebraic topology in an intuitive way. This time. What is...Alexander duality? Or: Horned spheres!? 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... Alexander duality. https://en.wikipedia.org/wiki/Alexand... https://mathoverflow.net/questions/41... More dualities and their history. https://www.math.purdue.edu/~gottlieb... Alexanders horned sphere. https://en.wikipedia.org/wiki/Alexand... https://mathworld.wolfram.com/Alexand... Jordan curve theorem and its generalizations. https://people.math.osu.edu/fiedorowi... https://en.wikipedia.org/wiki/Jordan_... https://mathworld.wolfram.com/JordanC... https://mathworld.wolfram.com/JordanC... https://math.stackexchange.com/questi... https://math.stackexchange.com/questi... Stereographic projection. https://en.wikipedia.org/wiki/Stereog... https://mathworld.wolfram.com/Stereog... Pictures used. https://marekbennett.files.wordpress.... https://demonstrations.wolfram.com/Th... https://exploringknots.files.wordpres... Hatcher’s book (I sometimes steal some pictures from there). https://pi.math.cornell.edu/~hatcher/... Always useful. https://en.wikipedia.org/wiki/Counter... Mathematica. https://demonstrations.wolfram.com/Gr... https://demonstrations.wolfram.com/Th... https://demonstrations.wolfram.com/St... https://demonstrations.wolfram.com/Th... #algebraictopology #topology #mathematics