Even triangulations of n–dimensional pseudo-manifolds

Rubinstein, J Hyam; Tillmann, Stephan

doi:10.2140/agt.2015.15.2949

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Even triangulations of $n$–dimensional pseudo-manifolds

J Hyam Rubinstein and Stephan Tillmann

Algebraic & Geometric Topology 15 (2015) 2947–2982

DOI: 10.2140/agt.2015.15.2949

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

Volume 15, issue 5 (2015)