# Questions tagged [topology]

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### Persistence diagram

Is there an easy way to get a persistence diagram of given planar points? For example the following points: ...
47 views

### Plot on fundamental square of a torus [duplicate]

I have line on the 2d plane, given by say f(t). I want to plot it in the torus by plotting Mod[f(t),2\[Pi]]. However, there are some sharp horizontal and vertical ...
141 views

### Finding radius when the hole is born and dead (persistence diagrams)

I have a list of vertices: ...
80 views

### Interfacing with an external computational homology program called CHomP

I have an external program called CHomP. I am trying to send a command to CHomP via RunThrough, and read the output string. It ...
313 views

### Check if two graphs have same shape

How can I check if two graphs have same shape or not? By shape I mean the two graphs are equivalent under a set of "name" replacements, like: ...
148 views

### Making 3D graphics showing sphere eversions

Were these pictures made by Mathematica or MATLAB? And how could I make ones like them?
144 views

### Computing the topological genus from a parametric function

Recall that the topological genus of a surface (or Euler characteristic) is (in essence) the number of its "holes." Thus the genus of a baseball is 0 while the genus of a donut or handled coffee cup ...
64 views

### Built-in functions for Homotopy group

Does Mathematica have built-in functions for Homotopy group, for example for computing $$\pi_n(S^m)=?$$ or more generally $n$-th homotopy group, $$\pi_n(X)=?$$ for some $X$. (I search, but I could ...
209 views

### Help to finish a Sperner lemma application

This is the code for the celebrated Sperner's Lemma in two dimensions --- which is equivalent to Brouwer Fixed Point theorem. Incidentally, it's my first program without any help --- until I ask this ...
46 views

### Compactness and Connectedness of sets

Can we check Compactness/Connectedness of sets in $R^{2}$ using some mathematica code ? If Yes , Can anyone tell how ?
1k views

### Plotting open balls for the given metric spaces [closed]

We're given a metric space (R,d) defined as follows: $$d(x,y) = |x-y|$$ We need to draw a open ball for this metric space with centre and radius of our choice. Open ball definition: For a fixed $x$ ...
632 views

### Small World network on a square grid

My aim is to generate a 2D Small World network on a square grid. i.e. 20x20. With a probability of 5%, one node rewires from an adjacent node to a random node of the grid, allowing some long distance ...
542 views

### Visualization of Homotopy equivalence between “heart curve” and zero

It is well-known that a "heart" is topologically equivalent to a "zero". where $$(x^2+y^2-1)^3=x^2y^3$$ is the heart equation; and $$\frac{x^2}{2}+\frac{y^2}{3}=1$$ is the equation of the zero shape (...
845 views

### ParametricPlot3D of Boy's surface

I'm trying to visualize Boy's surface using Bryant's parametrization, as per the MathWorld article. However, I'm not sure I understand the parametrization, and I don't know how to implement it when ...
997 views

### Package for symbolic computation of christoffel symbols and parallel transports in Riemannian geometry, given the metric

I've no knowledge in mathematica (but I do in matlab), but I'd really appreciate if someone could mention what is/are the best and easy to learn mathematica package(s) for symbolic and numerical (both,...
193 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 ...
296 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 ...
302 views

### Are there any built-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 built-in or third-party packages for general topology or algebraic topology in Mathematica? Through googling, I ...
1k views

### Finding minimal distance between two surfaces

This code will display two parametric surfaces: ...
497 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. ...
680 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 ...
3k views

### Homotopy Visualization

I noticed that both the lower cased 'i' and the Apple logo ļ£æ are topologically equivalent to the disjoint union of two closed discs. I'd like to animate a homotopy from the left to the right, can ...
1k 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 $S^2$ ...
2k views

### Morphing a “sheet of paper” into a torus

How can I visualize 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 ...
684 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 ...
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 \...