Dror Bar-Natan: Classes: 2003-04: Math 1350F - Knot Theory: (3) Next: Pathologies
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Some Non Obvious Examples

Which two are the same? (rendered using Rob Scharein's KnotPlot)

The Perko Pair: (are these the same?) (taken from http://www.math.cuhk.edu.hk/publect/lecture4/perko.html)

        

Is this the unknot? (From a book by A.B. Sossinsky. Thanks, Ian Agol)