How Does Knot Theory Connect with Other Fields and Real-World Applications?

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Knot theory intersects with various fields of mathematics, including topology and algebra, providing insights into the properties of space and shape. It has practical applications in biology, particularly in understanding DNA structure and behavior, as well as in chemistry for studying molecular structures. In physics, knot theory aids in the analysis of quantum field theories and the behavior of particles. Additionally, it finds relevance in computer science, particularly in algorithms related to data organization and network topology. Overall, knot theory serves as a crucial interdisciplinary tool with significant implications across multiple domains.
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How is knot theory involved in other fields of math? Any applications outside of math?
 
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Thread 'About the definition of topological manifold using closed sets'

We all know the definition of n-dimensional topological manifold uses open sets and homeomorphisms onto the image as open set in ##\mathbb R^n##. It should be possible to reformulate the definition of n-dimensional topological manifold using closed sets on the manifold's topology and on ##\mathbb R^n## ? I'm positive for this. Perhaps the definition of smooth manifold would be problematic, though.
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