Journal Article

On Quasi-homomorphisms and Commutators in the Special Linear Group over a Euclidean Ring

Masato Mimura

in International Mathematics Research Notices

Volume 2010, issue 18, pages 3519-3529
Published in print January 2010 | ISSN: 1073-7928
Published online February 2010 | e-ISSN: 1687-0247 | DOI: http://dx.doi.org/10.1093/imrn/rnq011
On Quasi-homomorphisms and Commutators in the Special Linear Group over a Euclidean Ring

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We prove that for any euclidean ring R and n ≥ 6, Γ = SLn(R) has no unbounded quasi-homomorphisms. By Bavard’s duality theorem, this means that the stable commutator length vanishes on Γ. The result is particularly interesting for R = F[x] for a certain field F (such as ℂ), because in this case the commutator length on Γ is known to be unbounded. This answers a question of M. Abért and N. Monod for n ≥ 6.

Journal Article.  2926 words.  Illustrated.

Subjects: Mathematics

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