I am trying to determine the fundamental group of the n-holed torus
I know that the fundamental group of the torus is $\mathbb{Z} \times \mathbb{Z}$
The n-holed torus deformation retracts onto n copies of the circle linked together (i.e. an extended version of the figure 9 loop - with n loops)
What would its fundamental group be?
I am guessing something of the form $\mathbb{Z} \times \mathbb{Z} \times .... \mathbb{Z} $