The Word Problem for Hyperbolic Groups

  • Tyler Taylor
  • Atish Mitra


Max Dehn's word problem asks us the following: Given a finitely generated group in terms of generators and relations, is there an algorithmic procedure to determine if an arbitrary word represents the identity element?  In this undergraduate research project, we define the notion of hyperbolicity of a metric space and present a geometric proof that all hyperbolic groups have solvable word problems.
Montana Academy of Sciences [Presentation Abstracts]