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)
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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.
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:
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)
Subtracting a solid knot from a 3-manifold (SUBTRACTION)
Creating a product manifold (MULTIPLICATION)
Creating manifolds from varieties, projective varieties and complex varieties.
Creating manifolds by specifying how to glue opposite faces of platonic solids.
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.