π₁(S¹) ≅ ℤ lacks motivation

Although Napkin spends considerable time preparing to prove $\pi_1(S^1) \cong \mathbb{Z}$, it doesn’t present any applications of this result. How about borrowing these two examples from [[Ha02]](https://pi.math.cornell.edu/~hatcher/AT/AT.pdf) and incorporating them somewhere in the book? <img width=500 src="https://github.com/user-attachments/assets/692aeaa6-2d51-48a7-89ff-6fe7280a5170"> <img width=500 src="https://github.com/user-attachments/assets/fc044c48-f4ac-4f89-a3db-05e4e12ca94e">