Fundamental group of the torus
= Fundamental group of the torus
For the standard longitude $a$ and meridian $b$,
$$
\pi_1(T^2)\cong\langle a,b\mid[a,b]=1\rangle\cong\mathbb Z^2.
$$
= Fundamental group of the torus
For the standard longitude $a$ and meridian $b$,
$$
\pi_1(T^2)\cong\langle a,b\mid[a,b]=1\rangle\cong\mathbb Z^2.
$$