So I'm trying to use Van Kampen theorem to prove that a space is null-homotopic.
The thing is I got it down to this $\langle a\mid a=1\rangle$, however I'm confused what does this mean.
For calculating the the torus you get it down to this $\langle a,b\mid a^{-1}b^{-1}ab=1\rangle \cong \mathbb{Z} \times \mathbb{Z}$.
But, was thinking does the brackets mean $\langle 1\rangle \cong \mathbb{Z}$ . I'm confused as normally the $\langle$ , $\rangle$ brackets means the generating set.