The Group Fixed by a Family of Injective Endomorphisms of a Free Group Paperback / softback
by Warren Dicks, Enric Ventura
Part of the Contemporary Mathematics series
Paperback / softback
Description
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.
Information
-
Item not Available
- Format:Paperback / softback
- Pages:81 pages, Illustrations
- Publisher:American Mathematical Society
- Publication Date:01/01/1996
- Category:
- ISBN:9780821805640
Other Formats
- PDF from £22.50
Information
-
Item not Available
- Format:Paperback / softback
- Pages:81 pages, Illustrations
- Publisher:American Mathematical Society
- Publication Date:01/01/1996
- Category:
- ISBN:9780821805640
