A note on groups of a family of hyperbolic tessellations

2014/02/18 by Anthony Gasperin, Gasperin, Anthony, Maurice Margenstern +1
Computer Science · #Cellular Automata and Applications #semigroups and automata theory #Algorithms and Data Compression

paper · pdf · doi:10.48550/arxiv.1402.4337

Abstract

In this paper we study the word problem of groups corresponding to tessellations of the hyperbolic plane. In particular using the Fibonacci technology developed by the second author we show that groups corresponding to the pentagrid or the heptagrid are not automatic.

Citations

• �ber unendliche diskontinuierliche Gruppen

Related

• Computation in word-hyperbolic groups
• The Geometry of Cycles in the Cayley Diagram of a Group
• Groups of piecewise isometric permutations of lattice points or finitary rearrangements of tessellations
• Hyperbolic jigsaws and families of pseudomodular groups II
• Boundaries of hyperbolic groups