Cofinality of the nonstationary ideal

We show that the reduced cofinality of the nonstationary ideal ${\mathcal N\! S}_\kappa$ on a regular uncountable cardinal $\kappa$ may be less than its cofinality, where the reduced cofinality of ${\mathcal N\! S}_\kappa$ is the least cardinality of any family ${\mathcal F}$ of nonstationary subsets of $\kappa$ such that every nonstationary subset of $\kappa$ can be covered by less than $\kappa$ many members of ${\mathcal F}$. For this we investigate connections of the various cofinalities of ${\mathcal N\! S}_\kappa$ with other cardinal characteristics of ${}^{\textstyle \kappa }\kappa$ and we also give a property of forcing notions (called manageability) which is preserved in ${<}\kappa$–support iterations and which implies that the forcing notion preserves non-meagerness of subsets of ${}^{\textstyle \kappa }\kappa$ (and does not collapse cardinals nor changes cofinalities).