6 research outputs found
Combinatorial 3-manifolds with transitive cyclic symmetry
In this article we give combinatorial criteria to decide whether a transitive
cyclic combinatorial d-manifold can be generalized to an infinite family of
such complexes, together with an explicit construction in the case that such a
family exists. In addition, we substantially extend the classification of
combinatorial 3-manifolds with transitive cyclic symmetry up to 22 vertices.
Finally, a combination of these results is used to describe new infinite
families of transitive cyclic combinatorial manifolds and in particular a
family of neighborly combinatorial lens spaces of infinitely many distinct
topological types.Comment: 24 pages, 5 figures. Journal-ref: Discrete and Computational
Geometry, 51(2):394-426, 201
Combinatorial Seifert fibred spaces with transitive cyclic automorphism group
In combinatorial topology we aim to triangulate manifolds such that their
topological properties are reflected in the combinatorial structure of their
description. Here, we give a combinatorial criterion on when exactly
triangulations of 3-manifolds with transitive cyclic symmetry can be
generalised to an infinite family of such triangulations with similarly strong
combinatorial properties. In particular, we construct triangulations of Seifert
fibred spaces with transitive cyclic symmetry where the symmetry preserves the
fibres and acts non-trivially on the homology of the spaces. The triangulations
include the Brieskorn homology spheres , the lens spaces
and, as a limit case, .Comment: 28 pages, 9 figures. Minor update. To appear in Israel Journal of
Mathematic
LIPIcs, Volume 258, SoCG 2023, Complete Volume
LIPIcs, Volume 258, SoCG 2023, Complete Volum
Simplicial manifolds, bistellar flips and a 16-vertex triangulation of the Poincaré homology 3-sphere
We present an algorithm based on bistellar operations that provides a useful tool for the construction of simplicial manifolds with few vertices. As an example, we obtain a 16-vertex triangulation of the Poincaré homology 3-sphere; we construct an infinite series of non-PL d-dimensional spheres with d+13 vertices for d 5; and we show that if a d-manifold admits any triangulation on n vertices, then it admits a non-combinatorial triangulation on n + 12 vertices (d 5)