On quasi-homomorphisms and commutators in the special linear group over a euclidean ring

研究成果: Article査読

2 被引用数 (Scopus)

抄録

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 ), 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.

本文言語English
ページ(範囲)3519-3529
ページ数11
ジャーナルInternational Mathematics Research Notices
2010
18
DOI
出版ステータスPublished - 2010
外部発表はい

ASJC Scopus subject areas

  • 数学 (全般)

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