It seems as though "nice" spaces don't have torsion in their homology groups. What is the underlying characteristic of these nice spaces; that they can be embedded in $\mathbb{R}^3$? So what are some examples of spaces which can be embedded in $\mathbb{R}^3$, but have torsion in their homology groups?
Torsion in homology groups of a topological space
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0@RonnieBrown : does a 2-dimensional cell complex corresponding to $G=\Bbb Z/2\Bbb Z$ embed in $\Bbb R^2$ or $\Bbb R^3$? – 2016-08-17