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The quadratic isoperimetric inequality for mapping tori of free group automorphisms. (English) Zbl 1201.20037
Mem. Am. Math. Soc. 955, xii, 152 p. (2010).
In this memoir the authors deal with the group $$F\rtimes_\varphi\mathbb{Z}$$, where $$\varphi$$ is an automorphism of the free group $$F$$. This group is called the algebraic mapping torus.
They prove, in their Main Theorem, that if $$F$$ is a finitely generated free group and $$\varphi$$ an automorphism of $$F$$, then $$F\rtimes_\varphi\mathbb{Z}$$ satisfies a quadratic isoperimetric inequality.
One of the corollaries says that the conjugacy problem for $$F\rtimes_\varphi\mathbb{Z}$$ is solvable, a result proved before.
This memoir has three parts. In Part 1, they prove the special case where $$\varphi$$ is a positive automorphism of $$F$$. Part 2 is dedicated to the construction and analysis of a refined topological representative for a suitable iterate of an arbitrary automorphism of a finitely generated free group. In Part 3 they use the techniques developed in Parts 1 and 2 to prove their Main Theorem.

##### MSC:
 20F65 Geometric group theory 20E36 Automorphisms of infinite groups 20E05 Free nonabelian groups 20F10 Word problems, other decision problems, connections with logic and automata (group-theoretic aspects) 57M07 Topological methods in group theory
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