Bridge number

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In a mathematical field of Knot theory, the Bridge number is an invariant of a knot. It is defined as the minimal number of bridges required in all the possible bridge representations of a knot. A bridge representation of a knot is a representation, such that the knot lies entirely in the plane apart for a couple of bridges whose projections onto the plane are straight lines.

It can be shown that every n-bridge knot can be decomposed into two trivial n-tangles and hence 2-bridge knots are rational knots.

[edit] Sources

Peter Cromwell, Knots and Links, Cambridge

[edit] Other invariants

• Linking coefficient
• Unknotting number
• Polygonal number

[edit] See also

• 2-bridge knot