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Tuesday, 28 November 2017: Joint ACiD/NODES Seminar

Sarah Rees (Newcastle, Maths): Rewriting in Artin groups

Time and Location:

13:00 in E360 (Durham)

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This is about the word problem in Artin groups.

For a group G = < X | R > defined (presented) by finite sets of generators and relations, the word problem is soluble if there is an algorithm which, given a word over X (ie string over X and its set of formal inverses) can decide whether or not w represents the identity element. In the 1950s, Novikov and Boone proved the existence of finitely presented groups with insoluble word problem.

Artin groups form a large and varied class of finitely presented groups (including free groups, free abelian groups, braid groups and much, much more) with many applications. Only some are known to have soluble word problem.

I’ll talk about attempts to solve the word problem in Artin groups, and in particular to find a general solution, that might work for the full spectrum of Artin groups. I’ll survey some background (which will include a definition of Artin groups), then discuss recent work of myself and Derek Holt, and of Patrick Dehornoy and Eddy Godelle.