Memoirs of the American Mathematical Society 2011; 104 pp; softcover Volume: 213 ISBN10: 0821869272 ISBN13: 9780821869277 List Price: US$74 Individual Members: US$44.40 Institutional Members: US$59.20 Order Code: MEMO/213/1004
 The authors develop a notion of axis in the CullerVogtmann outer space \(\mathcal{X}_r\) of a finite rank free group \(F_r\), with respect to the action of a nongeometric, fully irreducible outer automorphism \(\phi\). Unlike the situation of a loxodromic isometry acting on hyperbolic space, or a pseudoAnosov mapping class acting on Teichmüller space, \(\mathcal{X}_r\) has no natural metric, and \(\phi\) seems not to have a single natural axis. Instead these axes for \(\phi\), while not unique, fit into an "axis bundle" \(\mathcal{A}_\phi\) with nice topological properties: \(\mathcal{A}_\phi\) is a closed subset of \(\mathcal{X}_r\) proper homotopy equivalent to a line, it is invariant under \(\phi\), the two ends of \(\mathcal{A}_\phi\) limit on the repeller and attractor of the sourcesink action of \(\phi\) on compactified outer space, and \(\mathcal{A}_\phi\) depends naturally on the repeller and attractor. The authors propose various definitions for \(\mathcal{A}_\phi\), each motivated in different ways by train track theory or by properties of axes in Teichmüller space, and they prove their equivalence. Table of Contents  Introduction
 Preliminaries
 The ideal Whitehead graph
 Cutting and pasting local stable Whitehead graphs
 Weak train tracks
 Topology of the axis bundle
 Fold lines
 Bibliography
