Computation in word-hyperbolic groups

1998/11/03 by David B. A. Epstein, Epstein, David B. A., Derek F. Holt +1
Mathematics · #20F10 (secondary) #20F32 (primary) #FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR) #math.GR #math.GT #msc:20F10 #msc:20F32

paper · pdf · doi:10.48550/arxiv.math/9811012

23 pages, 7 figures, 2 tables

arxiv created 1998/11/03 · arxiv updated 2009/11/30

Abstract

We describe a procedure which verifies that a group given by generators and relators is word-hyperbolic. This procedure always works with a group which is word-hyperbolic, provided there is sufficient memory and time devoted to the problem. If the group is not word-hyperbolic, the procedure continues indefinitely. We also describe a procedure which computes the thinness of geodesic triangles in the Cayley graph of a word-hyperbolic group. Again this procedure is bound to work, given sufficient memory and time.

Related

• Polynomial-time proofs that groups are hyperbolic
• Boundaries of hyperbolic groups
• On the Definition of Word Hyperbolic Groups
• The generalised word problem in hyperbolic and relatively hyperbolic groups
• The compressed word problem in relatively hyperbolic groups