CUHK MATH Crossing number

Tie me up, Tie me down
 
Equivalence
Trefoil
Figure Eight
Whitehead
Trivial Knot
Perko Pairs
 
Classifications
Torus Knots
Alternating Knots
 
Invariants
Crossing number
Bridge number
Unknotting number
Tricolorability
Linking number
Polynomials

Many time, DON'T trust your first impression about crossing number. Here is an example to show how to reduce the crossing number.

It is a picture with apparently 5 crossing.
First step.
Second step.
Third step. Then, it is reduced to 4 crossing.


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