I am currently learning about stalks for the first time. In my exploration online about the topic, I routinely run into the same three examples:
- In a constant sheaf associated with an abelian group $A$, any stalk is isomorphic to $A$.
- In the sheaf of real-valued continuous functions, stalks are all germs at the given point.
- In the sheaf of complex-analytic functions, stalks are all germs at the given point.
I understand why these examples are ubiquitous. Stalks are about local behavior, and germs are an example of functions locally behaving the same being identified. Great!
That said, I would love to see more examples of stalks outside of these.