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Item Details
| Title:
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THE GROUP FIXED BY A FAMILY OF INJECTIVE ENDOMORPHISMS OF A FREE GROUP
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| By: |
Warren Dicks, Enric Ventura |
| Format: |
Paperback |
| List price:
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£24.95 |
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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: |
0821805649 |
| ISBN 13: |
9780821805640 |
| Publisher: |
AMERICAN MATHEMATICAL SOCIETY |
| Pub. date: |
1 January, 1996 |
| Series: |
Contemporary Mathematics No. 195 |
| Pages: |
81 |
| Description: |
Contains a proof of the Bestvina-Handel Theorem. By using the Bestvina-Handel argument with graph pullback techniques of J R Stallings, this title shows that, for any subgroup $H$ of $F$, the rank of the intersection $H\cap \mathrm {Fix}(\phi)$ is at most the rank of $H$. |
| Synopsis: |
This monograph contains a proof of the Bestvina-Handel Theorem (for any automorphism of a free group of rank $n$, the fixed group has rank at most $n$) that to date has not been available in book form. The account is self-contained, simplified, purely algebraic, and extends the results to an arbitrary family of injective endomorphisms. Let $F$ be a finitely generated free group, let $\phi$ be an injective endomorphism of $F$, and let $S$ be a family of injective endomorphisms of $F$.By using the Bestvina-Handel argument with graph pullback techniques of J. R. Stallings, the authors show that, for any subgroup $H$ of $F$, the rank of the intersection $H\cap \mathrm {Fix}(\phi)$ is at most the rank of $H$. They deduce that the rank of the free subgroup which consists of the elements of $F$ fixed by every element of $S$ is at most the rank of $F$. The topological proof by Bestvina-Handel is translated into the language of groupoids, and many details previously left to the reader are meticulously verified in this text. |
| Illustrations: |
Illustrations |
| Publication: |
US |
| Imprint: |
American Mathematical Society |
| Returns: |
Returnable |
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