# Questions tagged [computational-topology]

Computational topology is the study of decidability problems in topology and the algorithms that determine decidability. Examples of area of study include Normal Surface theory and the subproblems of unknot and $S^3$ recognition.

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### Is finding boundary-reducing discs for PL 3-manifolds with boundary pattern computationally efficient?

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### Are there structural properties of minimal torsion parts in simplicial complexes?

**1**

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### (Best) ways to reduce knot complexity?

**8**

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### Quantitative word problem for 3-manifold groups

**27**

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### Is being simply connected very rare?

**1**

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### Direct representation of simplical complexes in a HoTT implementation

**2**

**1**answer

### Uniform closure of a neighbourhood complex in the tritetragonal tiling

**3**

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### Looking through a bunch of links for unlinks?

**9**

**1**answer

### Smooth Morse function from Forman's discrete Morse function

**0**

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### Finite element method reference, from the perspective of the finite elements themselves

**3**

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### Motivation for persistent homology with respect to eigenfunctions of distance kernel operator in a recent preprint

**4**

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### Is there an upper bound on the number of points in point cloud for which we compute the persistent homology?

**3**

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### The complexity of cutting hackers in a computer network

**6**

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### Coarsifying persistence modules

**0**

**2**answers

### Representations of modular lattices, extension to cellular sheaves

**2**

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### Discrete Morse theory, choice of Morse function, and removing noise

**4**

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### Triangulations of 3-manifolds in Regina and SnapPy

**7**

**1**answer

### Products, coproducts and equalizers in category of lattices

**11**

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### Known obstruction for efficient computation of Stable homotopy groups?

**38**

**5**answers

### Reference on Persistent Homology

**2**

**1**answer

### On the entries of a matrix representation for a boundary operator of a persistence module

**18**

**3**answers

### Vietoris-Rips complex homology of a higher degree than the ambient dimension

**3**

**1**answer

### An algorithm to tell if two cut systems are handle slide equivalent?

**32**

**1**answer

### Why is persistent cohomology so much faster than persistent homology

**4**

**1**answer

### Complexity of computing the Vietoris-Rips complex

**10**

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### Computing the equivariant cohomology class of a Białynicki-Birula cell

**0**

**1**answer

### QUBO formulation of a discrete-variable Genetic Algorithm optimization problem

**0**

**1**answer

### Clarification of “death event” in persistent homology

**7**

**1**answer

### Computing homology of subvarieties of Euclidean spaces by persistent homology

**29**

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### What part is left unsolved in the Unknotting problem? (after results of Bar-Natan, Khovanov, Kronheimer and Mrowka)

**7**

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### Translation of Haken's paper “Theorie der Normalflächen”

**6**

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### Algorithm for computing the Arf invariant of a knot

**11**

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### Software for computing Thurston's unit ball

**17**

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### What is the state of the art for algorithmic knot simplification?

**35**

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### Inference using Topological Data Analysis: Is it worth it for a regular statistician to learn TDA?

**5**

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### Biggest ball included in an intersection of balls

**4**

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### Are there “geometrically nice” sets from which to construct coverings that admit “Vietoris-Rips like” approximations to the nerve?

**4**

**1**answer

### Triangulation of the surface determined by sampling two of its cross-sections

**22**

**3**answers

### Persistent homology of Gaussian fields in Euclidean space

**16**

**3**answers

### Computer-aided homology computations

**3**

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### Connected Sum Decomposition of a Knot

**2**

**2**answers

### Computational Topology Paper

**8**

**2**answers

### Homological computations

**10**

**4**answers

### Reference request for manifold learning

**29**

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