○室氏は男性と思われているみたいだね、レビューアーにｗｗｗ

In this article the author deals with the behaviour of
the conjecture under cabling and connected sum operations.
More precisely, he proves that if the conjecture holds
for $\scr K$ and $\scr L$ then it holds also for
the $(p,q)$-cable of $\scr K$ and for the connected
sum of $\scr K$ and $\scr L$. Moreover, he proves that
there are many examples of knots for which the inequality
is not sharp but the conjecture is still true. In fact,
he gives sufficient conditions on a closed braid representative
of a knot type in order not to have the sharpness of the
inequality for the knot type. Then he explicitly constructs,
via a block-strand diagram and using the enhanced Milnor number,
a family of knots satisfying these conditions and proves that,
in spite of this, for many of them the conjecture holds.