Goal.
Explaining basic concepts of algebraic topology in an intuitive way.
This time.
What is...the fundamental group? Or: How not to hang pictures on walls.
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.
www.dtubbenhauer.com/youtube.html
Website with exercises.
www.dtubbenhauer.com/lecture-algtop-2021.html
Material used.
Hatcher, Chapter 1
en.wikipedia.org/wiki/Fundamental_group
Awesome fundamental group animations (and other great stuff).
math.unice.fr/~indira/Mygifs.html
Circle pictures.
en.wikipedia.org/wiki/Fundamental_group#/media/File:Fundamental_group_of_the_circle.svg
Spivak’s hanging-pictures-puzzle (I stole some pictures from there).
arxiv.org/pdf/1203.3602.pdf
www.i-programmer.info/news/112-theory/3951-picture-hanging-puzzles.html
Hatcher’s book (I sometimes steal some pictures from there).
pi.math.cornell.edu/~hatcher/AT/AT.pdf
Always useful.
en.wikipedia.org/wiki/Counterexamples_in_Topology
#algebraictopology
#topology
#mathematics
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