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Results tagged with computational-topology
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user 5010
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.
24
votes
What part is left unsolved in the Unknotting problem? (after results of Bar-Natan, Khovanov,...
This isn't directly what you ask, but it's also worth noting that unknot detection is in $\text{NP} \cap \text{co-NP}$, that is, there are polynomial-checkable certificates that will show that either …
- 10.1k
41
votes
What part is left unsolved in the Unknotting problem? (after results of Bar-Natan, Khovanov,...
To strengthen Sam Nead's answer, note that it is trivial to compute the Jones polynomial from the Khovanov homology. It is known that computing (or even approximating) the Jones polynomial is #P-hard: …
- 10.1k