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5
votes
2answers
276 views

Morphing a “sheet of paper” into a torus

How can I visualise the standard topological "rubber-sheet" construction of a torus, that is, morphing a square into a torus? How can I start or are there any examples in the Mathematica ...
10
votes
1answer
287 views

Has anyone implemented cohomology for complex manifolds?

I'm investigating the cohomology of complex manifolds, and need to construct chain complexes, Mayer-Vietoris sequences etc. I use Mathematica for numerically tracing manifolds with geodesics, but ...
6
votes
3answers
621 views

Plotting the open ball for the post office metric space

The post office metric space, $P$ has the distance function defined as follows: $$ d_P (\mathbf{x},\mathbf{y}) := \begin{cases} 0 & \mathbf{x} = \mathbf{y}\\ \Vert \mathbf{x}\Vert_2+\Vert ...
12
votes
1answer
346 views

Generating a topological space diagram for an n-element set

Over on StackOverflow I asked a similar question for the n=3 case, but the answer given doesn't easily generalize. How can I make a diagram such as this: But for a general n-element space ...