What is...the 3d Poincaré conjecture?
Goal.
I would like to tell you a bit about my favorite theorems, ideas or concepts in mathematics and why I like them so much.
This time.
What is...the 3d Poincaré conjecture? Or: Its a sphere? Its a sphere!
Disclaimer.
Nobody is perfect, and I might have said something silly. If there is any doubt, then please check the references.
Slides.
http://www.dtubbenhauer.com/youtube.html
TeX files for the presentation.
https://github.com/dtubbenhauer/My-Te...
Thumbnail.
https://upload.wikimedia.org/wikipedi...
Main discussion.
https://doi.org/10.1090%2FS0273-0979-...
https://en.wikipedia.org/wiki/Analysi...)
https://www.maths.ed.ac.uk/~v1ranick/...
https://en.wikipedia.org/wiki/Poincar...
https://en.wikipedia.org/wiki/General...
https://www.jstor.org/stable/1970239?...
https://en.wikipedia.org/wiki/H-cobor...
https://mathworld.wolfram.com/h-Cobor...
Background material.
https://en.wikipedia.org/wiki/Geometr...
https://en.wikipedia.org/wiki/List_of...
https://en.wikipedia.org/wiki/Manifold
https://en.wikipedia.org/wiki/Knot_(m...)
https://en.wikipedia.org/wiki/Surface...)
https://en.wikipedia.org/wiki/3-manifold
https://en.wikipedia.org/wiki/3-sphere
https://en.wikipedia.org/wiki/Euclide...
https://en.wikipedia.org/wiki/Geometr...
https://en.wikipedia.org/wiki/Bing%E2...
Computer talk.
https://doc.sagemath.org/html/en/refe...
https://doc.sagemath.org/html/en/refe...
Pictures used.
https://en.wikipedia.org/wiki/Manifol...
https://en.wikipedia.org/wiki/Fore_%2...
Pictures from https://www.dtubbenhauer.com/lecture-...
https://en.wikipedia.org/wiki/Simply_...
https://en.wikipedia.org/wiki/Torus#/...
Pictures from the papers mentioned at https://en.wikipedia.org/wiki/Analysi...)
Picture from • What are...three manifolds?
https://www.rudyrucker.com/blog/image...
http://www.map.mpim-bonn.mpg.de/File:...
YouTube and co.
• Poincaré Conjecture - Numberphile
• What is the Poincare Conjecture? | World S...
• John Morgan, Perelman's work on the Poinca...
• What is...the Poincaré conjecture? (shameful self-promotion)
#topology
#geometry
#mathematics