On Algebraic Unknotting Numbers of Knots
SAEKI, Osamu
Tokyo J. of Math., Tome 22 (1999) no. 2, p. 425-443 / Harvested from Project Euclid
We show that the algebraic unknotting number of a classical knot $K$, defined by Murakami [9], is equal to the minimum number of unknotting operations necessary to transform $K$ to a knot with trivial Alexander polynomial. Furthermore, we define a new operation, called an elementary twisting operation, for smooth $(2n-1)$-knots with $n\geq 1$ and odd, and show that this is an unknotting operation for simple $(2n-1)$-knots. Moreover, the unknotting number of a simple $(2n-1)$-knot defined by using the elementary twisting operation is equal to the algebraic unknotting number of the $S$-equivalence class of its Seifert matrix if $n\geq 3$.
Publié le : 1999-12-15
Classification: 
@article{1270041448,
     author = {SAEKI, Osamu},
     title = {On Algebraic Unknotting Numbers of Knots},
     journal = {Tokyo J. of Math.},
     volume = {22},
     number = {2},
     year = {1999},
     pages = { 425-443},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1270041448}
}
SAEKI, Osamu. On Algebraic Unknotting Numbers of Knots. Tokyo J. of Math., Tome 22 (1999) no. 2, pp.  425-443. http://gdmltest.u-ga.fr/item/1270041448/