Combinatorial 3-manifolds with transitive cyclic symmetry.

Year of edition2011

 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.

 24 pages, 5 figures. Journal-ref: Discrete and Computational Geometry, 51(2):394-426, 2014

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