What is...homotopy?

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-algtop-2021.html

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

Möbius strip.
https://en.wikipedia.org/wiki/M%C3%B6bius_strip
https://math.stackexchange.com/questions/1839301/how-to-construct-a-homotopy-equivalence-between-a-mobius-band-and-a-circle

The house with two rooms.
https://sketchesoftopology.wordpress.com/2010/06/23/the-deformation-retraction-of-bings-house/
https://en.wikipedia.org/wiki/House_with_two_rooms

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

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

Видео What is...homotopy? канала VisualMath