  This paper introduces even triangulations of n-dimensional pseudo-manifolds
and links their combinatorics to the topology of the pseudo-manifolds. This is
done via normal hypersurface theory and the study of certain symmetric
representation. In dimension 3, necessary and sufficient conditions for the
existence of even triangulations having one or two vertices are given. For
Haken n-manifolds, an interesting connection between very short hierarchies and
even triangulations is observed.
