Boone-Higman embeddings of Aut(F_n) and mapping class groups of punctured surfaces

Jim Belk (University of Glasgow)

Monday 23rd March 15:00-16:00
Maths 311B

Abstract

The Boone-Higman conjecture asserts that every finitely presented group with solvable word problem embeds into a finitely presented simple group.  Such embeddings are now known for many classes of finitely presented groups, including arithmetic groups, right-angled Artin groups, Coxeter groups, hyperbolic groups, self-similar groups, Baumslag-Solitar groups, and free-by-cyclic groups. This talk will survey these results and then discuss some recent work with Francesco Fournier-Facio, James Hyde, and Matt Zaremsky that embeds each Aut(F_n) into a finitely presented simple group.  This also yields Boone-Higman embeddings for braid groups and many of their generalizations, including mapping class groups of punctured surfaces and several families of Artin groups.

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