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0
votes
0answers
16 views

The index number of an isolated critical point = 1+(e-h)/2 [migrated]

I know that the number of elliptic (e) and the number of hyperbolic should be even. But i find a difficulty in coming up with a proof for this
0
votes
1answer
107 views

Stitch edge of disk to edge of square in 3D space (with deformations) [closed]

Topologically each point on the edge of a square can be mapped uniquelly (including the corners?) to a point on the edge of a circle. It seems it might be possible to deform in 3D space the square ...
3
votes
3answers
205 views

I have a 2D space and I want to make it into a torus to replicate a paper

Suppose we have a 2D grid, divided by cells, and that we assign people to each cell. Each person has 4 neighbors, one in the cell above, another in the cell below, and neighbors in the cells to the ...
2
votes
0answers
62 views

Are there any build-in or third-party packages for general topology or algebraic topology in Mathematica?

I am learning general topology (wiki) and algebraic topology (wiki). Are there any build-in or third-party packages for general topology or algebraic topology in Mathematica? Or, what would ...
4
votes
2answers
429 views

Finding minimal distance between two surfaces

This code will display two parametric surfaces: ...
6
votes
1answer
313 views

Connect neighbouring points as list of segments in 2 D

Context I am interested in connecting neighboring points in 2/3D as list of segments. I am guessing this is something within the reach of graph theory, which is well implemented in mathematica. ...
13
votes
1answer
406 views

Morphological Filtering in 3D to produce skeletons

Context As a follow up of this question and that answer, I would like to identify the special lines separating 3D watersheds. These are useful in the context of astronomy to identify the ...
31
votes
4answers
1k views

Homotopy Visualization

I noticed that both the lower cased 'i' and the Apple logo  are topologically equivalent to the disjoint union of two closed discs. I'd like to animate a homeomorphism from the left to the right, ...
26
votes
1answer
674 views

Proving the hairy ball theorem using xAct

I would like to formally prove the hairy ball theorem in Mathematica, initially just for $S^2$, and then see about generalizing. An approach I thought about to use the xAct package to define $S^2$ ...
7
votes
2answers
590 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 ...
13
votes
1answer
405 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
959 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
443 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 ...