Failure of separation by quasi-homomorphisms in mapping class groups

Endo, H.; Kotschick, D.

doi:10.1090/S0002-9939-07-08866-1

Failure of separation by quasi-homomorphisms in mapping class groups
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by H. Endo and D. Kotschick PDF

Proc. Amer. Math. Soc. 135 (2007), 2747-2750 Request permission

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.

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