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arXiv · 1605.03682

Effective quasimorphisms on free chains

Jing Tao
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Abstract

We find homogeneous counting quasimorphisms that are effective at seeing chains in a free group F. As corollary, we derive that if a group G has an index-d free subgroup, then every element g in G either has stable commutator length at least 1/8d or some power of g is conjugate to its inverse. We also show that for a finitely-generated free group F, there is a countable basis for the real vector space of homogeneous quasimorphisms on F.

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Jing Tao. 2016-05-12. Effective quasimorphisms on free chains. https://arxiv.org/abs/1605.03682

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