相关论文: Dehn functions for mapping tori of amalgam of free…

The algebraic mapping torus $M_{\Phi}$ of a group $G$ with an automorphism $\Phi$ is the HNN-extension of $G$ in which conjugation by the stable letter performs $\Phi$. We classify the Dehn functions of $M_{\Phi}$ in terms of $\Phi$ for a…

By using a notion of a geometric Dehn twist in $\sharp_k(S^2 \times S^1)$, we prove that when projections of two $\mathbb{Z}$-splittings to the free factor complex are far enough from each other in the free factor complex, Dehn twist…

A criterion for quadratic or higher growth of group automorphisms is established which are represented by graph-of-groups automorphisms with certain well specified properties. As a consequence, it is derived (using results of a previous…

We study Dehn twists in the outer automorphism group of a finitely generated non-abelian free group. Our main result states that, under certain compatibility conditions, sufficiently large powers of finitely many Dehn twists generate a…

The mapping torus of an endomorphism \Phi of a group G is the HNN-extension G*_G with bonding maps the identity and \Phi. We show that a mapping torus of an injective free group endomorphism has the property that its finitely generated…

We study subgroups of the mapping class group of the torus generated by powers generated by powers of Dehn twists. We give a criterion to show when a collection of powers Dehn twists generates a free group using the ping pong lemma. We show…

McCarthy's Theorem for the mapping class group of a closed hyperbolic surface states that for any two mapping classes $\sigma,\tau \in \mathrm{Mod}(S)$ there is some power $N$ such that the group $\langle \sigma^N,\tau^N\rangle$ is either…

We prove that Thompson's group $T$ and, more generally, all the Higman-Thompson groups $T_n$ have quadratic Dehn function.

If F is a finitely generated free group and \phi is an automorphism of F then the mapping torus of \phi admits a quadratic isoperimetric inequality. This is the third and final paper in a series proving this theorem. The first two were…

If F is a finitely generated free group and \phi is an automorphism of F then F \rtimes_\phi Z satisfties a quadratic isoperimetric inequality.

We show that for each positive integer $k$ there exist right-angled Artin groups containing free-by-cyclic subgroups whose monodromy automorphisms grow as $n^k$. As a consequence we produce examples of right-angled Artin groups containing…

We prove that the Dehn function (that is, the smallest isoperimetric function) of the Richard Thompson's group F is quadratic.

We show that finitely generated mapping tori of free groups have a canonical collection of maximal sub-mapping tori of finitely generated free groups with respect to which they are relatively hyperbolic and locally relatively quasi-convex.…

We show that the Dehn function of the handlebody group is exponential in any genus $g\geq 3$. On the other hand, we show that the handlebody group of genus $2$ is cubical, biautomatic, and therefore has a quadratic Dehn function.

Let $G$ be the mapping torus of a polynomially growing automorphism of a finitely generated free group. We determine which epimorphisms from $G$ to $\mathbb{Z}$ have finitely generated kernel, and we compute the rank of the kernel. We thus…

We present necessary and sufficient conditions for the existence of a splitting over $\mathbb{Z}$ of the mapping torus $M_\phi=F\rtimes \mathbb{Z}$ of a free group automorphism $\phi$.

We prove that the mapping torus group $\FN \rtimes_{\alpha} \Z$ of any automorphism $\alpha$ of a free group $\FN$ of finite rank $n \geq 2$ is weakly hyperbolic relative to the canonical (up to conjugation) family $\mathcal H(\alpha)$ of…

If $F$ is a finitely generated free group and $\phi$ is a positive automorphism of $F$ then $F\rtimes_\phi Z$ satisfies a quadratic isoperimetric inequality.

Let a and b be two simple closed curves on an orientable surface S such that their geometric intersection number is greater than 1. It is known that the group generated by corresponding Dehn twists t_a and t_b is isomorphic to the free…

The homological and homotopical Dehn functions are different ways of measuring the difficulty of filling a closed curve inside a group or a space. The homological Dehn function measures fillings of cycles by chains, while the homotopical…