Axes in Outer Space
| dc.creator | Handel, Michael | |
| dc.creator | Mosher, Lee | |
| dc.date | 2006-05-13 | |
| dc.date | 2006-07-03 | |
| dc.date.accessioned | 2026-07-07T07:14:11Z | |
| dc.date.available | 2026-07-07T07:14:11Z | |
| dc.description | 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. | |
| dc.description | 96 pages. Version 2: The example of Section 3.4 has been corrected, and now has an even more interesting ideal Whitehead graph | |
| dc.identifier | https://arxiv.org/abs/math/0605355 | |
| dc.identifier | http://arxiv.org/abs/math/0605355 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/112775 | |
| dc.subject | Group Theory | |
| dc.subject | 20F65 57M07 | |
| dc.title | Axes in Outer Space | |
| dc.type | text |