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Item Details
| Title:
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AXES IN OUTER SPACE
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| By: |
Michael Handel, Lee Mosher |
| Format: |
Paperback |
| List price:
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£69.00 |
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We currently do not stock this item, please contact the publisher directly for
further information.
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| ISBN 10: |
0821869272 |
| ISBN 13: |
9780821869277 |
| Publisher: |
AMERICAN MATHEMATICAL SOCIETY |
| Pub. date: |
1 January, 2012 |
| Series: |
Memoirs of the AMS No. 1004 |
| Pages: |
104 |
| Description: |
"September 2011, volume 213, number 1004 (end of volume)." |
| Synopsis: |
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 Teichmuller 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 Teichmuller space, and they prove their equivalence. |
| Publication: |
US |
| Imprint: |
American Mathematical Society |
| Returns: |
Returnable |
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