Axes in Outer Space

Details Axes in Outer Space Axes in Outer Space

2006-05-13

arxiv.org/abs/math/0605355v2

Mathematics

Group Theory

96 pages. Version 2: The example of Section 3.4 has been corrected, and now has an even more interesting ideal Whitehead graph

Scientific paper

We develop a notion of axis in the Culler--Vogtmann outer space 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 pseudo-Anosov mapping class acting on Teichmuller space, X_r has no natural metric, and phi seems not to have a single natural axis. Instead our axes for phi, while not unique, fit into an ``axis bundle'' A_phi with nice topological properties: A_phi is a closed subset of X_r proper homotopy equivalent to a line, it is invariant under phi, the two ends of A_phi limit on the repeller and attractor of the source--sink action of phi on compactified outer space, and A_phi depends naturally on the repeller and attractor. We propose various definitions for A_phi, each motivated in different ways by train track theory or by properties of axes in Teichmuller space, and we prove their equivalence.

Affiliated with

Also associated with

No associations

Rating

Axes in Outer Space does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Axes in Outer Space, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Axes in Outer Space will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-264712