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The Group Fixed By A Family Of Injective Endomorphisms Of A Free Group (contemporary Mathematics) by Warren Dicks, Enric Ventura (ed.) is a nonfiction available to read on EtoBox.

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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.

Who reads The Group Fixed By A Family Of Injective Endomorphisms Of A Free Group (contemporary Mathematics)?

Author

Warren Dicks, Enric Ventura (ed.)

Publisher

American Mathematical Society

Published

1996

Language

EN

ISBN

9780821855324

Category

nonfiction

Subjects

Mathematics, Political Science, Stem