Cofinality of the nonstationary ideal

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