Related papers: Entropy and quasimorphisms

We prove that the full automorphism group and the outer automorphism group of the free group of countably infinite rank are coarsely bounded. That is, these groups admit no continuous actions on a metric space with unbounded orbits, and…

A homomorphism from a completely metrizable topological group into a free product of groups whose image is not contained in a factor of the free product is shown to be continuous with respect to the discrete topology on the range. In…

We study quasi-modular pseudometric spaces as asymmetric refinements of modular metric structures. To each such space we associate canonical forward and backward quasi-uniformities and the corresponding directional topologies. We introduce…

We determine the geometric structure of a minimal projective threefold having two `independent and commutative' automorphisms of positive topological entropy, and generalize this result to higher-dimensional smooth minimal pairs (X, G). As…

Let $\mathscr{F}=(M,\mathscr{L},E)$ be a Brody-hyperbolic singular holomorphic foliation on a compact complex manifold $M$. Suppose that $\mathscr{F}$ has isolated singularities and that its Poincar\'e metric is complete. This is the case…

We present a sheaf-theoretic construction of shape space -- the space of all shapes. We do this by describing a homotopy sheaf on the poset category of constructible sets, where each set is mapped to its Persistent Homology Transform (PHT).…

We study the dynamics of countable groups on their respective spaces of quasimorphisms. For cohomologically non-trivial quasimorphisms we show that there are no invariant measures and classify stationary measures. Within the equivalence…

We show that the Morse index of a closed minimal hypersurface in a four-dimensional Riemannian manifold cannot be bound in terms of the volume and the topological invariants of the hypersurface itself by presenting a method for constructing…

This paper addresses several isotopy problems on $4$-manifolds. First, we classify the isotopy classes of embeddings of $\Sigma$ in $\Sigma\times S^2$ that are geometrically dual to $\{\mbox{pt}\}\times S^2$, where $\Sigma$ is a closed…

The 1950's foundational literature on rational mechanics exhibits two somewhat distinct paradigms to the representation of continuous distributions of defects in solids. In one paradigm, the fundamental objects are geometric structures on…

We classify compact 2-connected homogeneous spaces with the same rational cohomology as a product of spheres. This classification relies on spectral sequences, homotopy theory, and representation theory. We then apply this classification to…

We define a natural topology on the collection of (equivalence classes up to scaling of) locally finite measures on a homogeneous space and prove that in this topology, pushforwards of certain infinite volume orbits equidistribute in the…

In \cite{Kramer11} Kramer proves for a large class of semisimple Lie groups that they admit just one locally compact $\sigma$-compact Hausdorff topology compatible with the group operations. We present two different methods of generalising…

We study the asymptotic behaviour of 1-parameter subgroups with respect to Hofer's metric when the underlying symplectic manifold is an open surface of infinite area. We prove that, depending on the topology of the level sets of the…

We study zero entropy automorphisms of a compact K\"ahler manifold $X$. Our goal is to bring to light some new structures of the action on the cohomology of $X$, in terms of the so-called dynamical filtrations on $H^{1,1}(X, {\mathbb R})$.…

For any infinite-type surface $S$, a natural question is whether the homology of its mapping class group contains any non-trivial classes that are supported on (i) a compact subsurface or (ii) a finite-type subsurface. Our purpose here is…

We prove that homological filling functions over a ring $R$ equipped with the discrete norm are quasi-isometry invariants for all groups of type $\mathrm{FP}_n$. This confirms a conjecture of Bader-Kropholler-Vankov in the case of discrete…

This survey/expository article covers a variety of topics related to the "topology at infinity" of noncompact manifolds and complexes. In manifold topology and geometric group theory, the most important noncompact spaces are often…

We construct a new type of locally homeomorphic quasiregular mappings in the 3-sphere and discuss their relation to the M.A.Lavrentiev problem, the Zorich map with an essential singularity at infinity, the Fatou's problem and a quasiregular…

Let $f\colon M \to M$ be a uniformly quasiregular self-mapping of a compact, connected, and oriented Riemannian $n$-manifold $M$ without boundary, $n\ge 2$. We show that, for $k \in \{0,\ldots, n\}$, the induced homomorphism $f^* \colon…