Even triangulations of $n$–dimensional pseudo-manifolds

Abstract

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.