A knot is called a hyperbolic knot if its complement is a hyperbolic space. Recall that a surface is called hyperbolic if it admits a Riemannian metric such that the Gaussian curvature is identical to . 375 more words
We first define some terms for links.
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A link is called a spilt link if there exists embedded in such that the sphere separate into two connected component and such that one component of is in , the other one is in .
*Ref : Cromwell
We should like to deal with links in a 2-dimensional sense. A linking diagram is a graph that contains the information of crossings of a link, and we can recover the original link by just looking at the 2-dimensional diagram. 1,457 more words
*Reference: Cromwell – Knots and Links
A knot is a subset of points homeomorphic to a circle .
Notice that the definition does not specify smoothness, so a knot can be represented as polygon (piecewise smooth) or just a smooth curve.1,259 more words