What are...Eilenberg-MacLane spaces?
Goal.
Explaining basic concepts of algebraic topology in an intuitive way.
This time.
What are...Eilenberg-MacLane spaces? Or: They are not spheres.
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...
Eilenberg-MacLane spaces.
https://en.wikipedia.org/wiki/Eilenbe...
https://ncatlab.org/nlab/show/Eilenbe...
Homotopy groups of spheres.
https://en.wikipedia.org/wiki/Homotop...
https://mathoverflow.net/questions/22...
https://mathoverflow.net/questions/64...
https://mathoverflow.net/questions/33...
Whitehead’s theorem.
https://en.wikipedia.org/wiki/Whitehe...
https://ncatlab.org/nlab/show/Whitehe...
Covering spaces and homotopy.
https://math.stackexchange.com/questi...
https://mathoverflow.net/questions/95...
Eilenberg-MacLane spaces represent cohomology.
https://encyclopediaofmath.org/wiki/E...
Elementary functions.
https://en.wikipedia.org/wiki/Element...
Pictures used.
https://web.ma.utexas.edu/users/richa...
https://en.wikipedia.org/wiki/Convex_...
https://en.wikipedia.org/wiki/Exponen...
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/Be...
#algebraictopology
#topology
#mathematics