Weight tests and hyperbolic groups

  title={Weight tests and hyperbolic groups},
  author={Guenther P Huck and Stephan Rosebrock and Andrew J. Duncan and Nicholas David Gilbert and James Howie},
The notion of reduced diagram plays a fundamental role in small cancellation theory and in tests for detecting asphericity of 2-complexes. By introducing vertex reduced as a stricter form of reducedness in diagrams we obtain a new combinatorial notion of asphericity for 2-complexes, called vertex asphericity, which generalizes diagrammatic reducibility and implies diagrammatic asphericity. This leads to a generalization and simpliication in applying the weight test 2] and the cycle test 6] 7… CONTINUE READING