All Questions
Tagged with computational-geometry computational-topology
10
questions
0
votes
0
answers
64
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Computational tasks resulting from Chern-Weil theory
I have recently learned Chern-Weil theory for smooth and complex manifolds, as well as surrounding material on cohomology with integral coefficients.
I am curious what computational tasks are ...
user30211
2
votes
0
answers
103
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Description of a point cloud being "undersampled" wrt persistent homology, confidence level?
I am completely new to topological data analysis, so I apologise if this is a well-known area of persistent homology, as well as for any imprecise language.
Suppose we know completely the topological ...
- 21
0
votes
0
answers
45
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Persistent diagrams for images : existing implementations or packages?
I am interest to compute the persistent diagram associated to the image of a persistent module as in ''Persistent Homology for Kernels, Images, and Cokernels'' : https://epubs.siam.org/doi/epdf/10....
- 73
-2
votes
1
answer
240
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Are there any non-elementary functions that are computable?
Does a function $\mathit{f}:\mathbb{R}→\mathbb{R}$ being non-elementary (not expressible as a combination of finitely many elementary operations), imply that it is not computable?
The particular case ...
- 11
15
votes
1
answer
355
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Are hyperbolic $n$-manifolds recursively enumerable?
Fixing a dimension $n \ge 4$, is the class of closed hyperbolic $n$-manifolds recursively enumerable?
Since hyperbolic manifolds are triangulable I can reformulate this in the following more explicit ...
- 3,369
5
votes
2
answers
348
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Is there an upper bound on the number of points in point cloud for which we compute the persistent homology?
I am interested in the topic of persistent homology (topological data analysis). According to what I read, there is some roadblock in the analysis of "big data" using persistent homology as it is ...
- 1,219
7
votes
1
answer
224
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Computing homology of subvarieties of Euclidean spaces by persistent homology
Let $M$ be a submanifold of the Euclidean space $\mathbb{R}^n$. Let $G$ be a finite group acting on $M$ freely. I want to compute the homology (or even the cohomology ring) of $M/G$.
Suppose the ...
- 543
5
votes
1
answer
548
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Biggest ball included in an intersection of balls
I would like to prove that for any family of balls $\{B(c_i,r_i)\}_i \subset \mathbb{R}^d$ such that $\{c_1, \dots, c_n\} \subset \bigcap_i B(c_i,r_i) $ and $\forall i, r_i \geq 1$, there exists a ...
- 153
5
votes
1
answer
234
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Triangulation of the surface determined by sampling two of its cross-sections
I have a data set that essentially looks like the picture below, i.e., it's given by sets of points in $\mathbb{R}^3$ that sample the cross-sections of a certain surface that in principle I do not ...
- 193
32
votes
4
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Computational software in Algebraic Topology?
I was wondering if there is any good software out there that allows you to do specific computations in algebraic topology. For example:
Create a simplicial complex/set and ask questions about its ...
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