# Effective quasimorphisms on free chains

@article{Tao2016EffectiveQO, title={Effective quasimorphisms on free chains}, author={J. Tao}, journal={arXiv: Group Theory}, year={2016} }

We find homogeneous counting quasimorphisms that are effective at seeing chains in a free group F. As corollary, we derive that if a groupG has an index–d free subgroup, then every element g ∈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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