Have you encountered the Seifert-Van Kampen Theorem yet?
How do you compute the Fundamental group of the connected sum of infinitely many tori?
I know the Fund. Group of the connected sum of n tori is given by
But what about the Fundamental group of the surface given by the connected sum of infinitely many tori, and how do you prove this?
yes, but I am not sure how to apply it here in this case. What would be the path connected open sets A and B whose union is the connected sum? Note, the connected sum is infinite, from the left and from the right, when drawing the space,...), and how to show their intersection is path connected?