Questions tagged [topology]

38 questions
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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 is 1. Is there a way to calculate the topological…
David G. Stork
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Persistent homology and Mathematica

I have a cloud of roughly 200 points in the plane. I would like to use Mathematica to draw the barcode corresponding to the corresponding persistent homology. There is a resource function PersistentHomology that does the trick (in…
Preem
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How can Mathematica be used to compute distance from a metric?

I have a metric: $$g_{\mu\nu}=\begin{bmatrix}-c & 0 & 0 & 0\\0 & a(t) & 0 & 0\\0 & 0 & a(t)\space r & 0\\0 & 0 & 0 & a(t)\space r\space \sinθ\end{bmatrix}$$ Having the dimensions $(t, r, θ, \phi)$. It corresponds to this…
Quark Soup
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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 ?
User9523
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