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Item Details
| Title:
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THE QUADRATIC ISOPERIMETRIC INEQUALITY FOR MAPPING TORI OF FREE GROUP AUTOMORPHISMS
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| By: |
Martin R. Bridson, Daniel Groves |
| Format: |
Paperback |
| List price:
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£73.00 |
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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: |
0821846310 |
| ISBN 13: |
9780821846315 |
| Publisher: |
AMERICAN MATHEMATICAL SOCIETY |
| Pub. date: |
15 February, 2010 |
| Series: |
Memoirs of the American Mathematical Society 203, No. 955 |
| Pages: |
152 |
| Description: |
Contains the proof of theorem which states that if F is a finitely generated free group and is an automorphism of F then it satisfies a quadratic isoperimetric inequality. This title focuses on the dynamics of the time flow of t-corridors. |
| Synopsis: |
The authors prove that if $F$ is a finitely generated free group and $\phi$ is an automorphism of $F$ then $F\rtimes_\phi\mathbb Z$ satisfies a quadratic isoperimetric inequality. The authors' proof of this theorem rests on a direct study of the geometry of van Kampen diagrams over the natural presentations of free-by-cylic groups. The main focus of this study is on the dynamics of the time flow of $t$-corridors, where $t$ is the generator of the $\mathbb Z$ factor in $F\rtimes_\phi\mathbb Z$ and a $t$-corridor is a chain of 2-cells extending across a van Kampen diagram with adjacent 2-cells abutting along an edge labelled $t$. The authors prove that the length of $t$-corridors in any least-area diagram is bounded by a constant times the perimeter of the diagram, where the constant depends only on $\phi$. The authors' proof that such a constant exists involves a detailed analysis of the ways in which the length of a word $w\in F$ can grow and shrink as one replaces $w$ by a sequence of words $w_m$, where $w_m$ is obtained from $\phi(w_{m-1})$ by various cancellation processes.In order to make this analysis feasible, the authors develop a refinement of the improved relative train track technology due to Bestvina, Feighn and Handel. Table of Contents: Positive automorphisms; Train tracks and the beaded decomposition; The General Case; Bibliography; Index. (MEMO/203/955) |
| Publication: |
US |
| Imprint: |
American Mathematical Society |
| Returns: |
Returnable |
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