Related papers: A metric Kan-Thurston theorem

We present a procedure of group cubization: It results in a group whose some features resemble the ones of a given group, and which acts without fixed points on a CAT(0) cubical complex. As a main application we establish lack of Kazhdan's…

Given a CAT(0) cube complex X, we show that if Aut(X) $\neq$ Isom(X) then there exists a full subcomplex of X which decomposes as a product with $\mathbb{R}^n$. As applications, we prove that if X is $\delta$-hyperbolic, cocompact and…

We extend the construction of the T-duality symmetry for the 2d compact boson to arbitrary values of the radius by including topological manipulations such as gauging continuous symmetries with flat connections. We show that the entire…

The notion of i-bounded geometry generalises simultaneously bounded geometry and the geometry of punctured torus Kleinian groups. We show that the limit set of a surface Kleinian group of i-bounded geometry is locally connected by…

We show the problem of counting homomorphisms from the fundamental group of a homology $3$-sphere $M$ to a finite, non-abelian simple group $G$ is #P-complete, in the case that $G$ is fixed and $M$ is the computational input. Similarly,…

Let $(X, g_0)$ be a simply connected, complete, negatively curved Riemannian manifold. We prove local and infinitesimal rigidity results for compactly supported deformations of the metric $g_0$. For any negatively curved metric $g$ equal to…

If a class of finitely generated groups Curly(G) is closed under isometric amalgamations along free subgroups, then every G in Curly(G) can be quasi-isometrically embedded in a group Hat(G) in Curly(G) that has no proper subgroups of finite…

We prove that if a sequence of geodesically complete CAT$(0)$-spaces $X_j$ with uniformly cocompact discrete groups of isometries converges in the Gromov-Hausdorff sense to $X_\infty$, then the dimension of the maximal Euclidean factor…

Collapsibility is a combinatorial strengthening of contractibility. We relate this property to metric geometry by proving the collapsibility of any complex that is CAT(0) with a metric for which all vertex stars are convex. This strengthens…

In a previous work, by extending the classical Quillen construction to the non-simply connected case, we have built a pair of adjoint functors, 'model' and 'realization', between the categories of simplicial sets and complete differential…

Let $T$ be a compact torus and $X$ be a a finite $T$-CW complex (e.g. a compact $T$-manifold). In earlier work, the second author introduced a functor which assigns to $X$ a so called GKM-sheaf $\mathcal{F}_X$ whose ring of global sections…

We determine the algebraic structure underlying the geometric complex associated to a link in Bar-Natan's geometric formalism of Khovanov's link homology theory (n=2). We find an isomorphism of complexes which reduces the complex to one in…

Let G be a locally compact group, let X be a universal proper G-space, and let Z be a G-equivariant compactification of X that is H-equivariantly contractible for each compact subgroup H of G. Let W be the resulting boundary. Assuming the…

Let $X$ be a CR manifold with transversal, proper CR $G$-action. We show that $X/G$ is a complex space such that the quotient map is a CR map. Moreover the quotient is universal, i.e. every invariant CR map into a complex manifold…

For a CAT(0) cube complex $\mathbf X$, we define a simplicial flag complex $\partial_\Delta\mathbf X$, called the \emph{simplicial boundary}, which is a natural setting for studying non-hyperbolic behavior of $\mathbf X$. We compare…

In this paper we focus on the set-open topologies on the group $\mathcal{H}(X)$ of all self-homeomorphisms of a topological space $X$ which yield continuity of both the group operations, product and inverse function. As a consequence, we…

Let T be a triangulated category, A a graded abelian category and h: T -> A a homology theory on T with values in A. If the functor h reflects isomorphisms, is full and is such that for any object x in A there is an object X in T with an…

Suppose a residually finite group $G$ acts cocompactly on a contractible complex with strict fundamental domain $Q$, where the stabilizers are either trivial or have normal $\mathbb{Z}$-subgroups. Let $\partial Q$ be the subcomplex of $Q$…

We introduce a $\mathbb{Z}$-valued cross ratio on Roller boundaries of ${\rm CAT(0)}$ cube complexes. We motivate its relevance by showing that every cross-ratio preserving bijection of Roller boundaries uniquely extends to a cubical…

This paper is devoted to the construction of norm-preserving maps between bounded cohomology groups. For a graph of groups with amenable edge groups we construct an isometric embedding of the direct sum of the bounded cohomology of the…