What is...Poincaré duality?

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

This time.
What is...Poincaré duality? Or: My face is 0-dimensional.

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...

Poincaré duality.
https://en.wikipedia.org/wiki/Poincar...
https://mathworld.wolfram.com/Poincar...
https://ncatlab.org/nlab/show/Poincar...
https://www.mathphysicsbook.com/mathe...

Platonic solids.
https://en.wikipedia.org/wiki/Platoni...
https://mathworld.wolfram.com/Platoni...

Dual graph.
https://en.wikipedia.org/wiki/Dual_graph
https://mathworld.wolfram.com/DualGra...

Dual polyhedron.
https://en.wikipedia.org/wiki/Dual_po...
https://mathworld.wolfram.com/DualPol...
https://archive.lib.msu.edu/crcmath/m...

Universal coefficient theorem.
https://en.wikipedia.org/wiki/Univers...
https://math.stackexchange.com/questi...

Pictures used.
https://en.wikipedia.org/wiki/Dual_po...
https://www.researchgate.net/profile/...
https://en.wikipedia.org/wiki/Torus#/...

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

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

Mathematica.
https://demonstrations.wolfram.com/Pl...

#algebraictopology
#topology
#mathematics