8vo (25 cm), IX, 83 pp. Publisher's laminated wrappers (minor shelf-wear). A self-contained research monograph presenting the first book-length proof of the Bestvina-Handel theorem, establishing that for any automorphism of a free group of rank n, the fixed subgroup has rank at most n, and extending the result to arbitrary families of injective endomorphisms. The authors reformulate the original topological argument in the language of groupoids, incorporating Stallings's graph pullback techniques to show that for any finitely generated free group F, injective endomorphism ?, and subgroup H of F, the rank of H ? Fix(?) does not exceed the rank of H; from this it follows that the subgroup fixed by a family S of injective endomorphisms has rank at most that of F. Four chapters treat groupoids and abstract maps of graphs, measuring devices including the Perron-Frobenius theorem and metric graphs, properties of the basic operations (collapsing, subdividing, folding), and minimal representatives and fixed subgroupoids, followed by open problems, bibliography, and index. A concise but influential contribution to combinatorial and geometric group theory.

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Bibliographic Details

Title

The Group Fixed by a Family of Injective Endomorphisms of a Free Group (Contemporary Mathematics)

Publisher

American Mathematical Society

Publication Date

1996

Language

English

ISBN 10

0821805649

ISBN 13

9780821805640

Binding

Soft cover

Condition

Fine

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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.
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.

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