Failure of separation by quasi-homomorphisms in mapping class groups

Abstract

We show that mapping class groups of surfaces of genus at least two contain elements of infinite order that are not conjugate to their inverses, but whose powers have bounded torsion lengths. In particular every homogeneous quasi-homomorphism vanishes on such an element, showing that elements of infinite order not conjugate to their inverses cannot be separated by quasi-homomorphisms.

4 pages

References in corpus (1)

• Quasi-homomorphisms and stable lengths in mapping class groups

Cited by in corpus (2)

• Higher-order signature cocycles for subgroups of mapping class groups and homology cylinders
• Stable commutator length in word-hyperbolic groups