Does there exist an example of a topological space $X$ which can be drawn, whose fundamental group is $S_3$? I know that every group is the fundamental group of a topological space, but I need a concrete example.
A topological space $X$ which can be $drawn$, whose fundamental group is $S_3$
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algebraic-topology
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3No example exists for any reasonable definition of "drawn". Even in the easier case of $S_2$ you can't actually draw the simplest example, the projective plane. – 2017-01-11
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0This question is a better fit for math.stackexchange. – 2017-01-11
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5@DanPetersen: you can "draw" the projective plane as an identification space. To me, this is a reasonable instance of being "drawn." – 2017-01-11
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1The questioner is not clear as to what 'drawn' is intended to mean. Please spell out more what your motivation is so that answers can be more helpful to you. – 2017-01-11
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0You say you need a concrete example -- but do you really need to *draw* one? :-) – 2017-01-11
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1The space of 3-element subsets of $\mathbb{R}^3$ might be what you're looking for. You can draw its points (sort of). – 2017-01-12