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arXiv · 0911.1341

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

Masato Mimura
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Abstract

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

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Masato Mimura. 2010-02-16. On Quasi-homomorphisms and Commutators in the Special Linear Group over a Euclidean Ring. https://doi.org/10.1093/imrn%2Frnq011

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