Stable length in stable groups

Abstract

We show that the stable commutator length vanishes for certain groups defined as infinite unions of smaller groups. The argument uses a group-theoretic analogue of the Mazur swindle, and goes back to the works of Anderson, Fisher, and Mather on homeomorphism groups.

Dedicated to Shigeyuki Morita on the occasion of his 60th birthday. To appear in Groups of Diffeomorphisms (Mathematical Society of Japan)

References in corpus (2)

• Conjugation-invariant norms on groups of geometric origin
• Stable commutator length in word-hyperbolic groups

Cited by in corpus (4)

• Conjugation-invariant norms on groups of geometric origin
• Quasi-morphisms on contactomorphism groups and contact rigidity
• Cancelation norm and the geometry of biinvariant word metrics
• Concordance group and stable commutator length in braid groups