Even triangulations of n–dimensional pseudo-manifolds

Rubinstein, J Hyam¹ ; Tillmann, Stephan²

¹Department of Mathematics and Statistics, The University of Melbourne, VIC 3010, Australia
²School of Mathematics and Statistics, The University of Sydney, NSW 2006, Australia

Algebraic and Geometric Topology, Tome 15 (2015) no. 5, pp. 2947-2982

Résumé

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.

Détail

DOI : 10.2140/agt.2015.15.2949

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

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