What is...the universal coefficient theorem?

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

This time.
What is...the universal coefficient theorem? Or: Working integrally rocks.

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.

Website with exercises.

Universal coefficients.

Relation to quantum physics.

Tor.

Hatcher’s book (I sometimes steal some pictures from there).

Always useful.

#algebraictopology
#topology
#mathematics
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Your videos have been very helpful - you are great at explaining this stuff...keep going!

hopefibration
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Q is torsion-free. A bijective map Z -> Q is given by Cantor’s snake. So that would mean H^n(X, Z) -> H^n(X, Q) is an isomorphism and Z-modules can be thought of in Q-vector spaces?

Jaylooker