The sheet number of a $2$-knot
is a quantity which reflects the complexity of the knotting in $4$-space.
The aim of this note is to determine the sheet numbers
of the $2$- and $3$-twist-spun trefoils.
For this purpose,
we give a lower bound of the sheet number
by the quandle cocycle invariant of a $2$-knot,
and an upper bound by the crossing number
of a $1$-knot.
Publié le : 2010-03-15
Classification:
2-knot,
diagram,
sheet,
triple point,
branch point,
57Q45,
57Q35
@article{1270645079,
author = {Satoh, Shin},
title = {A note on the sheet numbers of twist-spun knots},
journal = {Hiroshima Math. J.},
volume = {40},
number = {1},
year = {2010},
pages = { 1-15},
language = {en},
url = {http://dml.mathdoc.fr/item/1270645079}
}
Satoh, Shin. A note on the sheet numbers of twist-spun knots. Hiroshima Math. J., Tome 40 (2010) no. 1, pp. 1-15. http://gdmltest.u-ga.fr/item/1270645079/