Abstract We consider Calabi–Yau n -folds X arising from certain hyperplane arrangements. Using Fu–Vial’s theory of distinguished cycles for varieties with motive abelian type, we show that the subring Chow ring generated by divisors, Chern classes and intersections subvarieties positive codimension injects into cohomology. also prove Voisin’s conjecture , Voevodsky’s smash-nilpotence odd-dimens...

The residual torsion-free nilpotence of the commutator subgroup a knot group has played key role in studying bi-orderability groups. A technique developed by Mayland provides sufficient condition for to be residually-torsion-free nilpotent using work Baumslag. In this paper, we apply Mayland's several genus one pretzel knots and family with arbitrarily high genus. As result, obtain large number...