Algebraic Unknotting Number

The algebraic unknotting number of a knot K in S^3 is defined as the algebraic unknotting number of the S-equivalence class of a Seifert matrix of K. The algebraic unknotting number of an element in an S-equivalent class is defined as the minimum number of algebraic unknotting operations necessary to transform the element to the S-equivalence class of the zero matrix (Saeki 1999).

See also

Seifert Matrix, Unknotting Number

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Fogel, M. "Knots with Algebraic Unknotting Number One." Pacific J. Math. 163, 277-295, 1994.Murakami, H. "Algebraic Unknotting Operation, Q&A." Gen. Topology 8, 283-292, 1990.Saeki, O. "On Algebraic Unknotting Numbers of Knots." Tokyo J. Math. 22, 425-443, 1999.

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Algebraic Unknotting Number

Cite this as:

Weisstein, Eric W. "Algebraic Unknotting Number." From MathWorld--A Wolfram Web Resource.

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