On the model theory of the Free Factor Complex of rank 2
Zahra Mohammadi Khangheshlaghi, Katrin Tent
TL;DR
This paper studies the free factor complex of a rank 2 free group, providing an axiomatization of its theory and proving it is ω-stable with a unique prime model.
Contribution
It offers the first axiomatization of the free factor complex's theory for rank 2 and establishes its stability properties.
Findings
The theory of the free factor complex of rank 2 is ω-stable.
The prime model of this theory is AF_2.
Axiomatization of the theory is achieved for rank 2.
Abstract
We begin the investigation of the free factor complex of a free group of finite rank. For the case of rank 2 we axiomatize its theory and show that it is -stable with prime model .
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Taxonomy
TopicsAdvanced Topology and Set Theory · Homotopy and Cohomology in Algebraic Topology · Geometric and Algebraic Topology