1. The problem statement, all variables and given/known data What is the fundamental group of A where A is the 2-sphere with two disjoint disks removed. It has the same homotopy type as a familiar space. 2. Relevant equations 3. The attempt at a solution When I first looked at this problem, and saw how it was drawn out (in Munkres book,) it looked like a squashed sphere with two holes in it, so my first thought that it was homotopic to the double tours T#T. However, since the problem states that it is not the solid 2-sphere, I'm having second thoughts about it. To me it seems like its a sphere missing two holes in one hemisphere. It doesn't say anything about performing some surgery on the space and adding a cylinder or Mobius band to it, so it seems to me that it should be homotopic to the 2-sphere and therefore it's fundamental group is trivial. Am I on the right track here?