Let H be a cyclically-presented group on n generators with a single defining relator. Attempts have been made to classify such groups by their order, their status as a 3-manifold group, and the asphericity status of their presentations. For groups with a defining relator of length 3 these classifications are...
This is a program that searches for reduced spherical pictures over 1-generator, 1-relator relative group presentations with finite cyclic coefficient group. The search is depth-first and builds pictures face-by-face using a prescribed order. This program was written as part of Matthias Merzenich's PhD research. More details are available in the...
We present a method by which torsion-free groups of automorphisms of a 2-dimensional hyperbolic building which act simply transitively on the vertex set can be constructed, and prove that any such group can be obtained by this construction. The method produces groups defined by finite presentations with strong small cancellation...
This dataset contains the following:
1) A full list of the scaffolded presentations of the torsion-free vertex-regular lattices of Bourdon's building I55, classified up to isomorphism.
2) The source code for the programs used to construct these presentations in the software GAP 4.
3) The source code for the programs...
We describe two combinatorial problems in the theory of automorphism groups of compact Riemann surfaces of genus two or greater: enumerate the topological actions of a finite group on surfaces and determine the set of genera of surfaces admitting such a group action, called the genus spectrum. We illustrate results...
