Take the torus $T=S^{1} \times S^{1}$. Choose two points $x, y \in T$ and define a quotient topology by identifying $x$ and $y$. Let $X$ denote the quotient space. Prove that: a) Compute the fundamental group of $X$. b) Prove that $X$ is not homeomorphic to a surface.
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closed as too localized by GH, Dan Petersen, Igor Rivin, Andres Caicedo, Richard Kent May 3 2011 at 20:51 |
