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The compressed word problem in relatively hyperbolic groups

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I’ll talk about recent work with Derek Holt to prove the following result:

The compressed word problem for a group that is hyperbolic relative to a finite collection of free abelian subgroups is soluble in polynomial time.

This result extends the work of Lohrey and Schleimer proving the same results for free and hyperbolic groups. Our proof follows the same strategy, but has to work harder in order to relate the geometries of two different Cayley graphs, only one of which is locally finite. I’ll give some brief background to the compressed word problem and to to relatively hyperbolic groups, and attempt to give the flavour of the somewhat technical proof.

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

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