Mapping tori of free group automorphisms are coherent

The mapping torus of an endomorphism \Phi of a group G is the HNN-extension G*_G with bonding maps the identity and \Phi. We show that a mapping torus of an injective free group endomorphism has the property that its finitely generated subgroups are finitely presented and, moreover, these subgroups are of finite type.Comment: 17 pages, published versio

Abelian subgroups of \Out(F_n)

We classify abelian subgroups of Out(F_n) up to finite index in an algorithmic and computationally friendly way. A process called disintegration is used to canonically decompose a single rotationless element \phi into a composition of finitely many elements and then use these elements to generate an abelian subgroup A(\phi) that contains \phi. The main theorem is that up to finite index every abelian subgroup is realized by this construction. As an application we classify, up to finite index, abelian subgroups of Out(F_n) and of IA with maximal rank.Comment: 56 page

A Coordination-Theoretic Approach to Understanding Process Differences

Supporting human collaboration is challenging partly because of variability in how people work. Even within a single organization, there can be many variants of processes which have the same purpose. When distinct organizations must work together, the differences can be especially large, baffling and disruptive. Coordination theory provides a method and vocabulary for modeling complex collaborative activities in a way that makes both the similarities and differences between them more visible. We illustrate this, in this paper, by analyzing three engineering change management processes and demonstrating how our method compactly highlights the substantial commonalities and precise differences between what are on first glance are extremely divergent approaches

A McCool Whitehead type theorem for finitely generated subgroups of Out(Fn)\mathsf{Out}(F_n)

S. Gersten announced an algorithm that takes as input two finite sequences $\vec K=(K_1,\dots, K_N)$ and $\vec K'=(K_1',\dots, K_N')$ of conjugacy classes of finitely generated subgroups of $F_n$ and outputs: (1) $\mathsf{YES}$ or $\mathsf{NO}$ depending on whether or not there is an element $\theta\in \mathsf{Out}(F_n)$ such that $\theta(\vec K)=\vec K'$ together with one such $\theta$ if it exists and (2) a finite presentation for the subgroup of $\mathsf{Out}(F_n)$ fixing $\vec K$. S. Kalajd\v{z}ievski published a verification of this algorithm. We present a different algorithm from the point of view of Culler-Vogtmann's Outer space. New results include that the subgroup of $\mathsf{Out}(F_n)$ fixing $\vec K$ is of type $\mathsf{VF}$, an equivariant version of these results, an application, and a unified approach to such questions.Comment: 29 pages, 3 figure