Goal.
Explaining basic concepts of algebraic topology in an intuitive way.
This time.
What are...cell complexes? Or: Constructed from discs.
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.
Hatcher, Chapter 0
https://en.wikipedia.org/wiki/CW_complex
https://ncatlab.org/nlab/show/CW+complex
Hawaiian earring.
https://en.wikipedia.org/wiki/Hawaiian_earring
https://wildtopology.wordpress.com/2013/11/23/the-hawaiian-earring/
https://math.stackexchange.com/questions/3860464/showing-hawaiian-earrings-are-not-cw-complexes
https://math.stackexchange.com/questions/1236005/difference-between-wedge-of-countable-infinite-circle-and-hawaiian-ear-ring
https://math.stackexchange.com/questions/69698/wedge-sum-of-circles-and-hawaiian-earring?noredirect=1&lq=1
Pictures used.
https://www.mathphysicsbook.com/mathematics/topological-spaces/constructing-spaces/cell-complexes/
https://slideplayer.com/slide/11382479/
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