Paper 1, Section II, G
Let be the 2-dimensional torus. Let be the inclusion of the coordinate circle , and let be the result of attaching a 2-cell along .
(a) Write down a presentation for the fundamental group of (with respect to some basepoint), and identify it with a well-known group.
(b) Compute the simplicial homology of any triangulation of .
(c) Show that is not homotopy equivalent to any compact surface.
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