  A generic smooth map of a closed $2k$-manifold into $(3k-1)$-space has a
finite number of cusps ($\Sigma^{1,1}$-singularities). We determine the
possible numbers of cusps of such maps. A fold map is a map with singular set
consisting of only fold singularities ($\Sigma^{1,0}$-singularities). Two fold
maps are fold bordant if there are cobordisms between their source- and target
manifolds with a fold map extending the two maps between the boundaries, if the
two targets agree and the target cobordism can be taken as a product with a
unit interval then the maps are fold cobordant. We compute the cobordism groups
of fold maps of $(2k-1)$-manifolds into $(3k-2)$-space. Analogous cobordism
semi-groups for arbitrary closed $(3k-2)$-dimensional target manifolds are
endowed with Abelian group structures and described. Fold bordism groups in the
same dimensions are described as well.
