I need to find CW complex structure in the sphere by identifying the north and south pole.
First of all I tried to visualize what it looks like and if I am not wrong gluing the poles together will result in something looking sort of like a torus but without a hole. Now from a question that another user has posed namely(Cell Structure on Sphere with Two points identified) I saw that the CW complex structure is the following attach the boundary of the one cell to the zero cell and then attach the boundary of the two cell to the zero cell. To me this structure results to a wedge of a sphere and a circle because attaching the one cell to the zero cell gives a circle and then attaching the two cell to the zero cell will result to a sphere. As such this structure will result to the wedge of a sphere and a circle. Can you please explain to me what's wrong with my reasoning and how the structure above actually results to the sphere with the poles identified??
Thanks in advance