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Tunnel number
In mathematics, the tunnel number of a knot is a knot invariant, given by the minimal number of arcs (called tunnels) that must be added to the knot so that the complement becomes a handlebody. The tunnel number can equally be defined for links. The boundary of a regular neighbourhood of the union of the link and its tunnels forms a Heegaard splitting of the link exterior.
== Examples ==
* The unknot is the only knot with tunnel number 0.
* The trefoil knot has tunnel number 1.
Every link ''L'' has a tunnel number. This can be seen, for example, by adding a `vertical' tunnel at every crossing in a diagram of ''L''. It follows from this construction that the tunnel number of a knot is always less than or equal to its crossing number.
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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