Volume 15, issue 5 (2015)

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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
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
References
Publication
Received: 13 October 2014
Revised: 3 February 2015
Accepted: 5 February 2015
Published: 10 December 2015
Authors
J Hyam Rubinstein
Department of Mathematics and Statistics
The University of Melbourne
VIC 3010
Australia
Stephan Tillmann
School of Mathematics and Statistics
The University of Sydney
NSW 2006
Australia