Definition 20.2 (Lens spaces):

Let $Y = S^3 = \{(z, w) \in \mathbb{C}^2 / \vert z\vert^2 + \vert w\vert^2 = 1\}$ and $p$ be a prime, $q$ be an integer relatively prime to $p$. The action of $\mathbb{Z}_p$ on $S^3$ given by

$$\exp(2\pi i k/p)\cdot(z_1, z_2) = (\exp(2\pi i k/p)z_1, \exp(2\pi i kq/p)z_2)$$

is fixed point free and hence properly discontinuous. The orbit space is called the lens space denoted by $L(p, q)$. Theorem (20.2) now implies

$$\pi_1(L(p, q)) = \mathbb{Z}_p.$$