Related papers: Geometry and rigidity of mapping class groups

We study quotients of mapping class groups of punctured spheres by suitable large powers of Dehn twists, showing an analogue of Ivanov's theorem for the automorphisms of the corresponding quotients of curve graphs. Then we use this result…

We characterize convex cocompact subgroups of mapping class groups that arise as subgroups of specially embedded right-angled Artin groups. That is, if the right-angled Artin group G in Mod(S) satisfies certain conditions that imply G is…

We identify the smooth metrics $\mc{M}(M)$ on a manifold $M^n$ with the smooth isometric embeddings $f_g: (M,g) \rightarrow (\mb{S}^{\tn}, \tg)$ into a standard sphere of large dimension $\tn=\tn(n)$, and their Palais isotopic deformations,…

A contact twisted cubic structure (M,C,S) is a 5-dimensional manifold M together with a contact distribution C and a bundle S of twisted cubics that is compatible with the conformal symplectic form on C. In Engel's classical work, the Lie…

It is proved that the mapping class group of any closed surface with finitely many marked points is quasiisometric to a CAT(0) cube complex. We provide two distinct proofs, one tailored to mapping class groups, and one applying to a larger…

We show that for any lattice Veech group in the mapping class group $\mathrm{Mod}(S)$ of a closed surface $S$, the associated $\pi_1 S$--extension group is a hierarchically hyperbolic group. As a consequence, we prove that any such…

We define the class of high dimensional graph manifolds. These are compact smooth manifolds supporting a decomposition into finitely many pieces, each of which is diffeomorphic to the product of a torus with a finite volume hyperbolic…

We introduce and study the notion of relative rigidity for pairs $(X,\JJ)$ where 1) $X$ is a hyperbolic metric space and $\JJ$ a collection of quasiconvex sets 2) $X$ is a relatively hyperbolic group and $\JJ$ the collection of parabolics…

We study manifolds endowed with an (almost) even Clifford (hermitian) structure and admitting a large automorphism group. We classify them when they are simply connected and the dimension of the automorphism group is maximal, and also prove…

If $M$ is a closed Nil geometry 3-manifold then $\pi_1(M)$ is almost convex with respect to a fairly simple ``geometric'' generating set. If $G$ is a central extension or a ${\Bbb Z}$-extension of a word hyperbolic group, then $G$ is also…

The class of quasi-median graphs is a generalisation of median graphs, or equivalently of CAT(0) cube complexes. The purpose of this thesis is to introduce these graphs in geometric group theory. In the first part of our work, we extend the…

We define the strong shortcut property for rough geodesic metric spaces, generalizing the notion of strongly shortcut graphs. We show that the strong shortcut property is a rough similarity invariant. We give several new characterizations…

We consider here the $3$-sphere $\mathbf S^3$ seen as the boundary at infinity of the complex hyperbolic plane $\mathbf{H}^2_{\mathbf C}$. It comes equipped with a contact structure and two classes of special curves. First $\mathbf…

Geodesics and curvature of semidirect product groups with right invariant metrics are determined. In the special case of an isometric semidirect product, the curvature is shown to be the sum of the curvature of the two groups. A series of…

We generalize the notion of tight geodesics in the curve complex to tight trees. We then use tight trees to construct model geometries for certain surface bundles over graphs. This extends some aspects of the combinatorial model for doubly…

We show that for some negatively curved solvable Lie groups, all self quasiisometries are almost isometries. We prove this by showing that all self quasisymmetric maps of the ideal boundary (of the solvable Lie groups) are bilipschitz with…

We introduce a concept of tree-graded metric space and we use it to show quasi-isometry invariance of certain classes of relatively hyperbolic groups, to obtain a characterization of relatively hyperbolic groups in terms of their asymptotic…

In this work, we study the asymptotic geometry of the mapping class group and Teichmueller space. We introduce tools for analyzing the geometry of `projection' maps from these spaces to curve complexes of subsurfaces; from this we obtain…

We study graph products of groups from the viewpoint of measured group theory. We first establish a full measure equivalence classification of graph products of countably infinite groups over finite simple graphs with no transvection and no…

We demonstrate the quasi-isometry invariance of two important geometric structures for relatively hyperbolic groups: the coned space and the cusped space. As applications, we produce a JSJ-decomposition for relatively hyperbolic groups…