Even triangulations of n-dimensional pseudo-manifolds

TL;DR

This paper explores even triangulations of n-dimensional pseudo-manifolds, linking their combinatorial properties to topology through normal hypersurface theory and symmetric representations, with specific results in 3D and Haken manifolds.

Contribution

It introduces the concept of even triangulations in n-dimensional pseudo-manifolds and establishes conditions for their existence, connecting combinatorics with topology.

Findings

Necessary and sufficient conditions for 3D even triangulations with few vertices

Connection between short hierarchies and even triangulations in Haken n-manifolds

Development of a framework linking combinatorics and topology in 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.