Can we have more ways of constructing manifolds? #93
Description
In case I'm missing something there does not seem to be a whole lot of ways of constructing manifolds except for specifying the simplices.
I would expect things like:
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Taking quotients of manifolds over groups e.g.
$SO(4)/SO(3) = S^3$ . Or$\mathbb{R}^2/Z^2 = T^2$ (DIVISION) -
Gluing two manifolds together by take a sphere out of each one and gluing along the boundary. (ADDITION)
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Subtracting a solid knot from a 3-manifold (SUBTRACTION)
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Creating a product manifold (MULTIPLICATION)
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Creating manifolds from varieties, projective varieties and complex varieties.
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Creating manifolds by specifying how to glue opposite faces of platonic solids.
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Getting the manifold of any Lie group, eg. SU(6) or
$E_8$ (Albeit these are high dimensional).
Having some of these alternative ways of generating manifolds (which could then be triangulated) would be useful.