On ampleness and pseudo-Anosov homeomorphisms in the free group

Authors

RIZOS SKLINOS

DOI

10.3906/mat-1308-6

Abstract

We use pseudo-Anosov homeomorphisms of surfaces in order to prove that the first-order theory of non-Abelian free groups, T_{fg}, is n-ample for any n \in \omega. This result adds to the work of Pillay, which proved that T_{fg} is non-CM-trivial. The sequence witnessing ampleness is a sequence of primitive elements in F_{\omega}. Our result provides an alternative proof to the main result of a recent preprint by Ould Houcine and Tent.

Keywords

Free groups, pseudo-Anosov homeomorphisms, geometric stability theory

First Page

63

Last Page

80

Recommended Citation

SKLINOS, RIZOS (2015) "On ampleness and pseudo-Anosov homeomorphisms in the free group," Turkish Journal of Mathematics: Vol. 39: No. 1, Article 7. https://doi.org/10.3906/mat-1308-6
Available at: https://journals.tubitak.gov.tr/math/vol39/iss1/7