The Group Fixed by a Family of Injective Endomorphisms of a Free Group

Dicks, Warren, Ventura, Enric

ISBN 10: 0821805649 / ISBN 13: 9780821805640

Edité par American Mathematical Society, 1996

Pages intact with minimal writing/highlighting. The binding may be loose and creased. Dust jackets/supplements are not included. Stock photo provided. Product includes identifying sticker. Better World Books: Buy Books. Do Good. N° de réf. du vendeur 57848956-6

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.

Détails bibliographiques

Titre : The Group Fixed by a Family of Injective ...
Éditeur : American Mathematical Society
Date d'édition : 1996
Reliure : Couverture souple
Etat : Good