Goal.
Explaining basic concepts of algebraic topology in an intuitive way.

This time.
What is...homotopy? Or: The same shape!?

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...

Material used.
Hatcher, Chapter 0
https://en.wikipedia.org/wiki/Homotopy
https://en.wikipedia.org/wiki/Retract...)
https://ncatlab.org/nlab/show/homotopy

Möbius strip.
https://en.wikipedia.org/wiki/M%C3%B6...
https://math.stackexchange.com/questi...

The house with two rooms.
https://sketchesoftopology.wordpress....
https://en.wikipedia.org/wiki/House_w...

Latex and homotopy.
https://texample.net/tikz/examples/ho...

Hatcher’s book (I sometimes steal some pictures from there).
https://pi.math.cornell.edu/~hatcher/...

Always useful.
https://en.wikipedia.org/wiki/Counter...

#algebraictopology
#topology
#mathematics