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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What is the state of the art for algorithmic knot simplification?
Question: Given a `hard' diagram of a knot, with over a hundred crossings, what is the best algorithm and software tool to simplify it? Will it also simplify virtual knot diagrams, tangle diagrams, ...
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Reference on Persistent Homology
I will be teaching a course on algebraic topology for MSc students and this semester, unlike previous ones where I used to begin with the fundamental group, I would like to start with ideas of ...
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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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Persistent homology of Gaussian fields in Euclidean space
If you generate points in $\mathbb R^n$ via a process that respects a Gaussian normal distribution, then compute the persistent homology / barcodes, to my eye something fairly regular seems to be ...
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Deep learning for knot theory. Classification
As far as I know, there is a classification of all prime knots with less than 16 crossings.
It seems that there is already a fast enough algorithm to distinguish a knot from an unknot.
So in principle ...
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Homological computations
Suppose I have a group acting on some Hadamard manifold, and I want to understand as much as possible about the (co)homology of the quotient. In my case I can find a fundamental domain for the action ...
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Representations of modular lattices, extension to cellular sheaves
There are various "representation theorems" for lattices such as Birkhoff's Representation Theorem that states that every finite distributive lattice is isomorphic to a quasi-sublattice of the lattice ...
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