Definitions from topology

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I'm reading some papers on the unknotting problem in Knot theory and am running into some notation I don't know (my exposure to topology is minimal, but I have seen it in Analysis courses, Algebra, and just general reading). Suggestions on what to google to get a definition or the definitions themselves would be great. They are the following:

  • For a link K, what is N(K)?

  • For a disc D what is $\partial$D?

  • What is cl(*) (It appeared in the context of a surface S embedded in a 3-manifold M and cutting M along S to create a compact manifold cl(M-N(S)))

These things come up in several papers when I'm reading about Haken's algorithm. For example in here: http://people.maths.ox.ac.uk/lackenby/ekt11214.pdf

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To sum up the comments:

$N(K)$ is a tubular neighborhood of your knot, or surface, respectively.

$\text{cl}(A)$ is the closure of a set $A$.

$\partial D^2$ is the boundary circle of the disc $D^2$. Be careful: this is not the same as the notion of boundary of a subset of a space, but rather is a special case of the notion of the boundary of a manifold.