What is...a covering space?

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

This time.
What is...a covering space? Or: A topological Galois correspondence.

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...

Picture on the second slide which I forgot to come back to, stupid me.
A 2-sheet covering of the Klein bottle by a torus.

Material used.
Hatcher, Chapter 1
https://en.wikipedia.org/wiki/Coverin...


Torus and Klein bottle.
https://en.wikipedia.org/wiki/Torus
https://en.wikipedia.org/wiki/Klein_b...
https://math.stackexchange.com/questi...

Helix.
https://en.wikipedia.org/wiki/Helix

Finite fundamental groups.
https://math.stackexchange.com/questi...

Galois correspondence.
https://en.wikipedia.org/wiki/Fundame...

Pictures used.
https://en.wikipedia.org/wiki/Torus#/...
https://en.wikipedia.org/wiki/Klein_b...
https://en.wikipedia.org/wiki/Klein_b...
https://en.wikipedia.org/wiki/Coverin...

Awesome fundamental group animations (and other great stuff).
https://math.unice.fr/~indira/Mygifs....

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