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Título: Axes In Outer Space | |
| Autor: Handel, Michael; Lee Mosher | Precio: $1136.12 | |
| Editorial: American Mathematical Society | Año: 2011 | |
| Tema: Matematicas | Edición: 1ª | |
| Sinopsis | ISBN: 9780821869277 | |
| The authors develop a notion of axis in the Culler-Vogtmann outer space Xr of a finite rank free group Fr, with respect to the action of a nongeometric, fully irreducible outer automorphism ?. Unlike the situation of a loxodromic isometry acting on hyperbolic space, or a pseudo-Anosov mapping class acting on Teichmüller space, Xr has no natural metric, and ? seems not to have a single natural axis. Instead these axes for ?, while not unique, fit into an "axis bundle" A? with nice topological properties: A? is a closed subset of Xr proper homotopy equivalent to a line, it is invariant under ?, the two ends of A? limit on the repeller and attractor of the source-sink action of ? on compactified outer space, and A? depends naturally on the repeller and attractor.
The authors propose various definitions for A?, each motivated in different ways by train track theory or by properties of axes in Teichmüller space, and they prove their equivalence. |
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