Regular isotopy

Regular isotopy

In the mathematical subject of knot theory, a regular isotopy of a link diagram is the equivalence relation generated by using the 2nd and 3rd Reidemeister moves only. The notion of regular isotopy was introduced by Louis Kauffman (Kauffman 1990). It can be thought of as an isotopy of a ribbon pressed flat against the plane which keeps the ribbon flat. This is a finer equivalence relation than ambient isotopy of a framed link, since the 2nd and 3rd Reidemeister moves preserve the winding number of the diagram (Kauffman 1990, pp.450ff.).

ee also

*ambient isotopy
*Kauffman polynomial

Notes

References

L. H. Kauffman: "An invariant of regular isotopy", "Transactions of the American Mathematical Society" 318(2), 1990, pp.317-371


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