Polynomial-time proofs that groups are hyperbolic

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• Colva Roney-Dougal (University of St Andrews)
• Friday 21 February 2020, 13:45-14:45
• CMS, MR13.

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A finitely-presented group G is hyperbolic if there is a linear bound on the number of relators required to prove that a word of length n is equal to the identity in G. This talk will present some efficient, low-degree polynomial-time procedures which seek to prove that a given finitely-presented group is hyperbolic. For those presentations on which these procedures succeed, we have further procedures which construct, in low-degree polynomial time, a linear time word problem solver and a quadratic time conjugacy problem solver. The class of finite presentations on which these procedures are successful include all presentations satisfying any of the standard small cancellation conditions, but also many others.

This talk is part of the Geometric Group Theory (GGT) Seminar series.

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