Voir la notice de l'article provenant de la source Mathematical Sciences Publishers
A pretzel knot K is called odd if all its twist parameters are odd and mutant ribbon if it is mutant to a simple ribbon knot. We prove that the family of odd 5–stranded pretzel knots satisfies a weaker version of the slice-ribbon conjecture: all slice odd 5–stranded pretzel knots are mutant ribbon, meaning they are mutant to a ribbon knot. We do this in stages by first showing that 5–stranded pretzel knots having twist parameters with all the same sign or with exactly one parameter of a different sign have infinite order in the topological knot concordance group and thus in the smooth knot concordance group as well. Next, we show that any odd 5–stranded pretzel knot with zero pairs or with exactly one pair of canceling twist parameters is not slice.
Keywords: slice, ribbon, pretzel, knot, Donaldson's theorem, d-invariant
Bryant, Kathryn 1
@article{10_2140_agt_2017_17_3621,
author = {Bryant, Kathryn},
title = {Slice implies mutant ribbon for odd 5{\textendash}stranded pretzel knots},
journal = {Algebraic and Geometric Topology},
pages = {3621--3664},
publisher = {mathdoc},
volume = {17},
number = {6},
year = {2017},
doi = {10.2140/agt.2017.17.3621},
url = {http://geodesic.mathdoc.fr/articles/10.2140/agt.2017.17.3621/}
}
TY - JOUR AU - Bryant, Kathryn TI - Slice implies mutant ribbon for odd 5–stranded pretzel knots JO - Algebraic and Geometric Topology PY - 2017 SP - 3621 EP - 3664 VL - 17 IS - 6 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.2140/agt.2017.17.3621/ DO - 10.2140/agt.2017.17.3621 ID - 10_2140_agt_2017_17_3621 ER -
%0 Journal Article %A Bryant, Kathryn %T Slice implies mutant ribbon for odd 5–stranded pretzel knots %J Algebraic and Geometric Topology %D 2017 %P 3621-3664 %V 17 %N 6 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.2140/agt.2017.17.3621/ %R 10.2140/agt.2017.17.3621 %F 10_2140_agt_2017_17_3621
Bryant, Kathryn. Slice implies mutant ribbon for odd 5–stranded pretzel knots. Algebraic and Geometric Topology, Tome 17 (2017) no. 6, pp. 3621-3664. doi: 10.2140/agt.2017.17.3621
Cité par Sources :