Groups, periodic planes and hyperbolic buildings

Details Groups, periodic planes and hyperbolic buildings Groups, periodic planes and hyperbolic buildings

2003-07-30

arxiv.org/abs/math/0307380v1

Mathematics

Combinatorics

Scientific paper

We give an elementary construction of polyhedra whose links are connected bipartite graphs, which are not necessarily isomorphic pairwise. We show, that the fundamental groups of some of our polyhedra contain surface groups. In particular, we construct polyhedra whose links are generalized $m$-gons. The polyhedra of this type are interesting because of their universal coverings, which are two-dimensional hyperbolic buildings with different links. The presentation of the results is done in the language of combinatorial group theory.

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