Related papers: Outer automorphism groups of hyperbolic groups, bo…

A group $G$ is called subgroup conjugacy separable if for every pair of non-conjugate finitely generated subgroups of $G$, there exists a finite quotient of $G$ where the images of these subgroups are not conjugate. It is proved that the…

We prove that the mapping class group of a sphere with five punctures admits uncountably many coarsely equivariant coarse median structures. The same is shown for right-angled Artin groups whose defining graphs are connected, triangle- and…

The outer automorphism group Out(G) of a group G acts on the set of conjugacy classes of elements of G. McCool proved that the stabilizer $Mc(c_1,...,c_n)$ of a finite set of conjugacy classes is finitely presented when G is free. More…

Let $G$ be a hyperbolic group that splits as a graph of free groups with cyclic edge groups. We prove that, unless $G$ is isomorphic to a free product of free and surface groups, every finite abelian group $M$ appears as a direct summand in…

For X = R, C, or H it is well known that cusp cross-sections of finite volume X-hyperbolic (n+1)-orbifolds are flat n-orbifolds or almost flat orbifolds modelled on the (2n+1)-dimensional Heisenberg group N_{2n+1} or the (4n+3)-dimensional…

We classify the 3-dimensional hyperbolic polyhedral orbifolds that contain no embedded essential 2-suborbifolds, up to decomposition along embedded hyperbolic triangle orbifolds (turnovers). We give a necessary condition for a 3-dimensional…

We find the automorphism group of the moduli space of parabolic bundles on a smooth curve (with fixed determinant and system of weights). This group is generated by: automorphisms of the marked curve, tensoring with a line bundle, taking…

We show that the outer automorphism group of a polycyclic-by-finite group is an arithmetic group. This result follows from a detailed structural analysis of the automorphism groups of such groups. We use an extended version of the theory of…

We show that the automorphism group of the disk complex is isomorphic to the handlebody group. Using this, we prove that the outer automorphism group of the handlebody group is trivial.

In this paper, we classify the three-dimensional contact partially hyperbolic diffeomorphisms whose stable, unstable and central distributions are smooth, and whose non-wandering set equals the whole manifold. We prove that up to a finite…

We give three necessary and sufficient conditions so that a parabolic holomorphic semigroup $(\phi_t)$ in the unit disc is of finite shift. One is in terms of the asymptotic behavior of speeds of convergence, the second one is related to…

We prove that every endomorphism of the mapping class group of an orientable surface onto a subgroup of finite index is in fact an automorphism.

An automorphism of a group is called outer if it is not an inner automorphism. Let $G$ be a finite $p$-group. Then for every outer $p$-automorphism $\phi$ of $G$ the subgroup $C_G(\phi)=\{x\in G \;|\; x^\phi=x\}$ has order $p$ if and only…

For a finite group G of Lie type and a prime p, we compare the automorphism groups of the fusion and linking systems of G at p with the automorphism group of G itself. When p is the defining characteristic of G, they are all isomorphic,…

A rigid automorphism of a linking system is an automorphism which restricts to the identity on the Sylow subgroup. A rigid inner automorphism is conjugation by an element in the center of the Sylow subgroup. At odd primes, it is known that…

We prove that the outer automorphism group of a free group of countably infinite rank is complete.

Sela proved every torsion-free one-ended hyperbolic group is coHopfian. We prove that there exist torsion-free one-ended hyperbolic groups that are not commensurably coHopfian. In particular, we show that the fundamental group of every…

See math.CV/0509030 which replaces this paper.

We define and study the class of inner ultrahomogeneous groups, which includes Hall's universal group and the universal locally recursively presentable group. We provide simple criteria for ample generic automorphisms, straight maximality,…

We find strictly ascending HNN extensions of finite rank free groups possessing a presentation 2-complex which is a non positively curved square complex. On showing these groups are word hyperbolic, we have by results of Wise and Agol that…