Goal.
Explaining basic concepts of algebraic topology in an intuitive way.
This time.
What is...Whitehead’s Theorem? Or: A perfect invariant!?
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
Whitehead’s theorem.
https://en.wikipedia.org/wiki/Whitehead_theorem
https://ncatlab.org/nlab/show/Whitehead+theorem
(Co)homological Whitehead’s theorem.
https://math.stackexchange.com/questions/750955/homology-whitehead-theorem-for-non-simply-connected-spaces
https://math.stackexchange.com/questions/3241160/finding-a-counter-example-of-the-whitehead-theorem
https://math.stackexchange.com/questions/717018/cohomological-whitehead-theorem
Topologists sine curve.
https://en.wikipedia.org/wiki/Topologist%27s_sine_curve
https://en.wikipedia.org/wiki/Shape_theory_(mathematics)#Warsaw_Circle
Pictures used.
https://en.wikipedia.org/wiki/Convex_set#/media/File:Convex_polygon_illustration1.svg
https://i.stack.imgur.com/yYLkv.png
https://math.stackexchange.com/questions/696533/quasi-circle-is-not-contractible
https://en.wikipedia.org/wiki/N-sphere#/media/File:Sphere_wireframe.svg
https://en.wikipedia.org/wiki/File:Hypersphere.png
https://en.wikipedia.org/wiki/Real_projective_plane#/media/File:ProjectivePlaneAsSquare.svg
https://www.researchgate.net/profile/Giorgio-Sonnino/publication/287250322/figure/fig1/AS:386176071553025@1469082958707/The-Projective-Space-RP-n-1-is-diffeomorphic-to-S-n-1-made-by-the-Upper-hemisphere.png
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
Mathematica.
https://mathworld.wolfram.com/WhiteheadsTheorem.html
#algebraictopology
#topology
#mathematics