More homology computations | Algebraic Topology | NJ Wildberger
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- čas přidán 10. 10. 2012
- In our last lecture, we introduced homology explicitly in the very simple cases of the circle and disk. In this lecture we tackle the 2-sphere. First we compute the homology using the model of a tetrahedron: four 2-dimensional faces, but no 3-dim solid. This illustrates how linear algebra naturally arises in this kind of problem.
We then provide a much simpler alternative calculation using the more flexible framework of semi-simplicial complexes, or delta-complexes, where only two triangular faces are needed, and the calculation is much simplified, however still giving the same final result (which by the way is that H_0 (S^2)=Z, H_1 (S^2)=0 and H_2 (S^2)=Z, with all higher homology groups being 0.
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Very helpful for learning homology group. I have been confused by homology for a long time until now. The concrete examples are very illustrative. Thank you.
You simply saved my life! This was an awesome lecture.
This is what remedial math of any college education should start with
AlgTop lectures helped me a lot. Thank you.
You explain very well, the first class on homology was very useful. However, for these more complicated examples, I think it's better to use singular homology. You can easily compute the reduced singular homology groups of S^n using a bunch of strong theorems.
very nice lecture..............many many thanks to you.
I'm always keen to find out how calculating the Homology of spaces can be put to practical uses. Even if it involves looking at complicated spaces using a computer.
Excellent lecture - cleared up things that had been confusing me. Thanks!
What's shown here are the absolute fundamentals. It just goes to show how badly taught your AG course must have been. I've been there myself.
Awesome!
very nice ... thank you very much
Just 2 class and then may be i can make my tesis, thanks
You're a lifesaver
thanks