I have started reading "Differential Forms in Algebraic Topology" by Bott, Tu, recently. While I'm quite happy with the exposition of the theorems and explanation of theoretical results, I'm missing examples in many places.
There are some exercises in the text, which for example ask one to compute cohomology of the Möbius band or the Euler class of the tautological bundle on $\mathbb C P^n$. However, I'm having some difficulty with this, in particular I'm never really sure, whether I'm doing things the right way.
I would therefore like to take a look at some examples of concrete computations, so I could get some kind of guidance on how to do it.
So I was wondering whether there is a book which contains many examples or maybe there are some ressources on the internet that I've been unable to find?
Thanks in advance for any pointers!
Edit: Maybe I should add that the topic of the book is not so much general algebraic topology.
The table of contents reads:
- De Rham Theory
- Cech-de Rham Complex
- Spectral Sequences and Applications
- Characteristic Classes
Throughout the book one is working with differentiable manifolds.