Volume 15, issue 5 (2015)

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Even triangulations of $n$–dimensional pseudo-manifolds

J Hyam Rubinstein and Stephan Tillmann

Algebraic & Geometric Topology 15 (2015) 2947–2982
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.

Keywords
3-manifold, n-manifold, triangulation, even triangulation, normal surface, normal hypersurface, representations of the fundamental group
Mathematical Subject Classification 2010
Primary: 57M25, 57N10, 57M60, 57Q15