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

modnarandom · 2013-08-31T07:50:56+00:00

How is knot theory involved in other fields of math? Any applications outside of math?

Thread '2-sphere intrinsic definition by gluing disks' boundaries'

A sphere as topological manifold can be defined by gluing together the boundary of two disk. Basically one starts assigning each disk the subspace topology from ##\mathbb R^2## and then taking the quotient topology obtained by gluing their boundaries. Starting from the above definition of 2-sphere as topological manifold, shows that it is homeomorphic to the "embedded" sphere understood as subset of ##\mathbb R^3## in the subspace topology.

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Thread '2-sphere intrinsic definition by gluing disks' boundaries'

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