Axes in Outer Space
Seiten
2012
American Mathematical Society (Verlag)
978-0-8218-6927-7 (ISBN)
American Mathematical Society (Verlag)
978-0-8218-6927-7 (ISBN)
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The authors develop a notion of axis in the Culler-Vogtmann 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 pseudo-Anosov 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 source-sink 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.
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.
Michael Handel is at CUNY, Herbert H. Lehman College, Bronx, NY
Reihe/Serie | Memoirs of the American Mathematical Society |
---|---|
Verlagsort | Providence |
Sprache | englisch |
Gewicht | 190 g |
Themenwelt | Mathematik / Informatik ► Mathematik ► Geometrie / Topologie |
ISBN-10 | 0-8218-6927-2 / 0821869272 |
ISBN-13 | 978-0-8218-6927-7 / 9780821869277 |
Zustand | Neuware |
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